41. Front: Math.GT Geometric Topology Preprints in geometric topology in the Arxiv. http://front.math.ucdavis.edu/math.GT

Front for the arXiv Mon, 1 Nov 2010 Front math GT search register submit journals ... iFAQ math.GT Geometric Topology Calendar Search Atom feed Search Author Title/ID Abstract+ Category articles per page Show Search help Recent New articles (last 12) 1 Nov arXiv:1010.6257 The lens space realization problem. Joshua Evan Greene math.GT 1 Nov arXiv:1010.6236 Classifying Voronoi graphs of hex spheres. Aldo-Hilario Cruz-Cota math.GT math.MG 1 Nov arXiv:1010.6200 A tree traversal algorithm for decision problems in knot theory and 3-manifold topology. Benjamin A. Burton , Melih Ozlen math.GT cs.CG 29 Oct arXiv:1010.5814 Classification of broken Lefschetz fibrations with small fiber genera. R. Inanc Baykur , Seiichi Kamada math.GT math.SG 28 Oct arXiv:1010.5719 Labeled Rauzy classes and framed translation surfaces. Corentin Boissy math.GT math.DS Cross-listings 1 Nov arXiv:1010.6295 Hilbert series of algebras associated to direct graphs and order homology. Vladimir Retakh , Shirlei Serconek , Robert Wilson math.RA math.GT 29 Oct arXiv:1010.6043 The fundamental group of random 2-complexes. Eric Babson , Christopher Hoffman , Matthew Kahle J. Amer. Math. Soc.

42. Topology - Wiktionary A branch of mathematics studying those properties of a geometric figure or solid that are not changed by stretching, bending and similar homeomorphisms. (topology) A http://en.wiktionary.org/wiki/topology

topology Definition from Wiktionary, the free dictionary Jump to: navigation search Contents English Pronunciation Noun Synonyms ... edit English edit Pronunciation RP IPA /təˈpɒləʤi/ SAMPA /t"@pQl@dZi/ GenAm IPA /təˈpɑːləʤi/ SAMPA /t"@pA:l@dZi/ Wikipedia has an article on: Topology Wikipedia edit Noun topology plural topologies mathematics A branch of mathematics studying those properties of a geometric figure or solid that are not changed by stretching bending and similar homeomorphisms topology A collection of subsets of a set X such that the empty set and X are both members of and is closed under arbitrary unions and finite intersections medicine The anatomical structure of part of the body. computing The arrangement of nodes in a communications network technology The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application. edit Synonyms mathematics analysis situs edit Holonyms topological space edit Meronyms open set edit Derived terms point-set topology algebraic topology geometric topology edit Related terms topological topological space topologically topologist ... edit Translations study of geometric properties that are not changed by stretching etc.

43. Topology Atlas Preprints, abstracts, calendar, links, other resources. http://at.yorku.ca/topology/

Topology Atlas is a publisher of information related to topology. What's New Search Preprints Abstracts ... About Topology Atlas Favorites: Topology Q+A Board Upcoming Conferences Topology Proceedings Lecture Notes

44. Topology s and illustrations of several topological and differential geometry related notions....... http://www.chez.com/alcochet/toposi.htm

TOPOLOGY Here are fundamental objects of the lacanian topology : The M�bius band The torus The Klein bottle The cross-cap The borromean knot Topology is a branch of pure mathematics, deals with the fundamental properties of abstract spaces. Whereas classical geometry is concerned with measurable quantities, such as angle, distance, area, and so forth, topology is concerned with notations of continuity and relative position. Point-set topology regards geometrical figures as collections of points, with the entire collection often considered a space. Combinatorial or algebraic topology treats geometrical figures as aggregates of smaller building blocks. BASIC CONCEPTS In general, topologists study properties of spaces that remain unchanged, no matter how the spaces are bent, stretched, shrunk, or twisted. Such transformations of ideally elastic objects are subject only to the condition that nearby points in one space correspond to nearby points in transformed version of that space. Because allowed deformation can be carried out by manipulating a rubber sheet, topology is sometimes known as rubber-sheet geometry. In contrast, cutting, then gluing together parts of a space is bound to fuse two or more points and to separate points once close together. The basic ideas of topology surfaced in the mid-19th century as offshoots of algebra and ANALYTIC GEOMETRY. Now the field is a major mathematical pursuit, with applications ranging from cosmology and particle physics to the geometrical structure of proteins and other molecules of biological interest.

45. Topology F alls C onnect. High Quality Network Cabling . Design and Installation. 330821-5756. karl@fallsconnect.com . Network Topologies. THERE ARE THREE PRIMARY TYPES OF NETWORK TOPOLOGIES, WHICH http://fallsconnect.com/topology.htm

F alls C onnect High Quality Network Cabling Design and Installation karl@fallsconnect.com Network Topologies THERE ARE THREE PRIMARY TYPES OF NETWORK TOPOLOGIES, WHICH REFER TO THE PHYSICAL AND LOGICAL LAYOUT OF THE NETWORK CABLING. THEY ARE BUS, STAR AND RING. BUS AND STAR ARE THE MOST WIDELY USED FOR ETHERNET NETWORKS AND RING IS USED FOR TOKEN RING NETWORKS. Low Level Standards Prior to discussing network topologies, it is necessary to define low level standards. These are guidelines that describe how data (frames) are transmitted across the physical and data link layers of a network. They are developed by the Institute of Electrical and Electronic Engineers. The 802.x standard describes guidelines for Ethernet and Token Ring networks. Standards such as 10 BASE T and 10 BASE 2 describe a specific cable type and other limitations for Ethernet, such as Category 5 unshielded twisted pair for 100 BASE T, or Fast Ethernet. Bus topology Advantages Less expensive than a star topology due to less footage of cabling and no network hubs Good for smaller networks not requiring higher speeds Disadvantages Limited in size and speed One bad connector can take down entire network Difficult to troubleshoot Star Topology In a star topology, each network device has a home run of cabling back to a network hub, giving each device a separate connection to the network. If there is a problem with a cable, it will generally not affect the rest of the network. The most common cable media in use for star topologies is unshielded twisted pair copper cabling. Category 3 is still found frequently in older installations. It is capable of 10 megabits per second data transfer rate, making it suitable for only 10 BASE T Ethernet. Most new installations use Category 5 cabling. It is capable of data transfer rates of 100 megabits per second, enabling it to employ 100 BASE T Ethernet, also known as Fast Ethernet. More importantly, the brand new 1000 BASE T Ethernet standard will be able to run over most existing Category 5. Finally, fiber optic cable can be used to transmit either 10 BASE T or 100 BASE T Ethernet frames.

46. Oleg Viro's Home Page Draft version includes several papers on algebraic geometry. http://www.math.uu.se/~oleg/educ-texts.html

Oleg Viro's home page texts for students about myself mathematics for students talks ... Elementary Topology. Textbook in Problems, by O.Ya.Viro, O.A.Ivanov, V.M.Kharlamov and N.Y.Netsvetaev. Configurations of Skew Lines in the 3-Dimensional Space by J.Viro and O.Viro This is about links made of lines. One has to require that the lines are not only disjoint, but also non-parallel. This gives the lines an ability to be linked with each other. As long as the number of lines is not large (less than 6), the linking numbers rule. Then the Jones polynomial comes. On a horizont the Khovanov homology can be recognized... Introductions into Topology of Real Algebraic Varieties Introductions to patchworking Dequantization of real algebraic geometry on logarithmic paper A talk by Oleg Viro at the Third European Congress of Mathematicians (Barcelona, 2000). It bridged patchworking and Litvinov - Maslov dequantization of positive real numbers and started up a broad development of Tropical geometry. What is an Amoeba? Notices AMS, pdf On Euler's footsteps, Evgeny Shchepin's Uppsala lectures on Calculus.

47. Topology -- Britannica Online Encyclopedia topology, branch of mathematics, sometimes referred to as “rubber sheet geometry,” in which two objects are considered equivalent if they can be continuously deformed into http://www.britannica.com/EBchecked/topic/599686/topology

document.write(''); Search Site: Advanced Search With all of these words With the exact phrase With any of these words Without these words Home SHOP BROWSE BLOG ... HELP Username: Password: Remember me Forgot your password? Help Email " is the e-mail address you used when you registered. Password " is case sensitive. If you need additional assistance, please contact customer support Enter the e-mail address you used when enrolling for Britannica Premium Service and we will e-mail your password to you. topology My Britannica CREATE MY topology NEW ARTICLE ... SAVE topology Table of Contents: topology Article Article Basic concepts of general topology Basic concepts of general topology - Simply connected Simply connected - Topological equivalence Topological equivalence - Homeomorphism Homeomorphism - Topological structure Topological structure - - Topological space Topological space - - Continuity Continuity Algebraic topology Algebraic topology - Fundamental group Fundamental group - Differential topology Differential topology - Knot theory Knot theory History of topology History of topology Additional Reading Additional Reading Year in Review Links Year in Review Links Related Articles Related Articles External Web sites External Web sites Citations Article Basic concepts of general topology Simply connected Topological equivalence ... Citations Primary Contributor: Stephan C. Carlson

48. Network Topologies - Webopedia.com All devices are connected to one another in the shape of a closed loop, so that each device is connected directly to two other devices, one on either side of it. Tree topology http://www.webopedia.com/quick_ref/topologies.asp

Webopedia.com Sign Up Sign In Search Term of the Day Recent Terms Did You Know? Quick Reference ... Quick Reference > Network Topologies Network Topologies Posted: 06-24-2010 , Last Updated: 07-06-2010 More Terms operating system Webopedia Weekly Stay up to date on the latest developments in internet terminology with a free weekly newsletter from Webopedia. Join to subscribe now. Sign up Already a member? Log in now Webopedia is a part of the Internet.com network. Topology refers to the shape of a network , or the network's layout. How different nodes in a network are connected to each other and how they communicate are determined by the network's topology. Topologies are either physical or logical . Below are diagrams of the five most common network topologies. Mesh Topology Devices are connected with many redundant interconnections between network nodes . In a true mesh topology every node has a connection to every other node in the network. Star Topology Sponsored You're Not Ready For Internal Cloud: You can fast-track cloud learning, but delivering an internal cloud will take years for most enterprises. Learn more.

49. Project First Algorithm Analysis University and NASA site dealing with specific topology and algorithm analysis. http://www.projectfirst.org/

50. UCSB Mathematics Staff The Department of Mathematics, UCSB, homepage. Geometric topology is often split into low dimensional (4 or less) and high http://math.ucsb.edu/department/topology.php

51. Fibrewise General Topology: A Brief Outlook By David Buhagiar A brief outlook by David Buhagiar. http://at.yorku.ca/t/a/i/c/34.htm

Topology Atlas Document # taic-34 Topology Atlas Invited Contributions vol. 5 issue 1 (2000) 1-4 Fibrewise General Topology: A Brief Outlook David Buhagiar Invited Contribution The study of General Topology is usually concerned with the category TOP of topological spaces as objects, and continuous maps as morphisms. The concepts of space and map are equally important and one can even look at a space as a map from this space onto a singleton space and in this manner identify these two concepts. With this in mind, a branch of General Topology which has become known as General Topology of Continuous Maps, or Fibrewise General Topology, was initiated. This field of research is concerned most of all in extending the main notions and results concerning topological spaces to those of continuous maps. In this way one can see some well-known results in a new and clearer light and one can also be led to further developments which otherwise would not have suggested themselves. The fibrewise viewpoint is standard in the theory of fibre bundles, however, it has been recognized relatively recently that the same viewpoint is also as important in other areas such as General Topology. For an arbitrary topological space Y one considers the category TOP Y TOP , since the category TOP is isomorphic to the particular case of TOP Y in which the space Y is a singleton space.

52. Topology - Elsevier topology publishes papers in many parts of mathematics, but with special emphasis on subjects which are related to topology or geometry, such as• Global analysis and global http://www.elsevier.com/wps/find/journaldescription.cws_home/261/description

53. General Topology Gudunov Database and tables explaining the logical mesh. http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=5934854

54. Intute - Topology Collection of GT home pages. http://www.intute.ac.uk/sciences/cgi-bin/browse.pl?id=25620

55. Topology - Uncyclopedia, The Content-free Encyclopedia topology is a particularly virulent, yet fortunately rare, strain of mathematics. http://uncyclopedia.wikia.com/wiki/Topology

56. Topology And Its Applications - Elsevier A journal concerned with publishing original research papers. http://www.elsevier.com/wps/find/journaldescription.cws_home/505624/description#

57. Understanding Topology And Shapefiles Esri is the world leader in GIS (geographic information system) modeling and mapping software and technology. This site features GIS mapping software, desktop GIS, server GIS http://www.esri.com/news/arcuser/0401/topo.html

Store Contact Us Careers Home ... Partners Understanding Topology and Shapefiles by David M. Theobald, Colorado State University When asked if topology is a key concept of GIS, most GIS users will nod their heads in agreement. But ask these same folks about how topology is handled in shapefiles and the nodding heads give way to shrugging shoulders. Why should GIS users care about topology? What are the advantages and disadvantages of storing polygon data in shapefiles rather than coverages? What Is Topology? "Conundrum Inspires Topology." More recently, the United States Census Bureau, while preparing for the 1970 census, pioneered the application of mathematical topology to maps to reduce the errors in tabulating massive amounts of census data. Today, topology in GIS is generally defined as the spatial relationships between adjacent or neighboring features. Mathematical topology assumes that geographic features occur on a two-dimensional plane. Through planar enforcement, spatial features can be represented through nodes (0-dimensional cells); edges, sometimes called arcs (one-dimensional cells); or polygons (two-dimensional cells). Because features can exist only on a plane, lines that cross are broken into separate lines that terminate at nodes representing intersections rather than simple vertices. In GIS, topology is implemented through data structure. An ArcInfo coverage is a familiar topological data structure. A coverage explicitly stores topological relationships among neighboring polygons in the Arc Attribute Table (AAT) by storing the adjacent polygon IDs in the LPoly and RPoly fields. Adjacent lines are connected through nodes, and this information is stored in the arc-node table. The ArcInfo commands, CLEAN and BUILD, enforce planar topology on data and update topology tables.

58. What Is Algebraic Topology? Introductory essay by Joe Neisendorfer, University of Rochester. http://www.math.rochester.edu/people/faculty/jnei/algtop.html

WHAT IS ALGEBRAIC TOPOLOGY? THE BEGINNINGS OF ALGEBRAIC TOPOLOGY Algebraic topology is a twentieth century field of mathematics that can trace its origins and connections back to the ancient beginnings of mathematics. For example, if you want to determine the number of possible regular solids, you use something called the Euler characteristic which was originally invented to study a problem in graph theory called the Seven Bridges of Konigsberg. Can you cross the seven bridges without retracing your steps? No and the Euler characteristic tells you so. Later, Gauss defined the so-called linking number, a precise invariant which tells you whether two circles are linked. It is called an invariant because it remains the same even if we continuously deform the geometric object. Gauss also found a relationship between the total curvature of a surface and the Euler characteristic. All of these ideas are bound together by the central idea that continuous geometric phenomena can be understood by the use of discrete invariants. The winding number of a curve illustrates two important principles of algebraic topology. First, it assigns to a geometric odject, the closed curve, a discrete invariant, the winding number which is an integer. Second, when we deform the geometric object, the winding number does not change, hence, it is called an invariant of deformation or, synomynously, an invariant of homotopy.

59. What Is Network Topology? Definition From WhatIs.com In communication networks, a topology is a usually schematic description of the arrangement of a network, including its nodes and connecting lines. http://searchnetworking.techtarget.com/sDefinition/0,,sid7_gci213156,00.html

network topology HOME SEARCH BROWSE BY CATEGORY BROWSE BY ALPHABET ... WHITE PAPERS Search our IT-specific encyclopedia for: Browse alphabetically: A B C D ... Network Hardware network topology What is a network topology? In communication networks, a topology is a usually schematic description of the arrangement of a network, including its nodes and connecting lines. There are two ways of defining network geometry: the physical topology and the logical (or signal) topology. The physical topology of a network is the actual geometric layout of workstations. There are several common physical topologies, as described below and as shown in the illustration. In the bus network topology, every workstation is connected to a main cable called the bus . Therefore, in effect, each workstation is directly connected to every other workstation in the network. In the star network topology, there is a central computer or server to which all the workstations are directly connected. Every workstation is indirectly connected to every other through the central computer. In the ring network topology, the workstations are connected in a closed loop configuration. Adjacent pairs of workstations are directly connected. Other pairs of workstations are indirectly connected, the data passing through one or more intermediate nodes.

60. The Geometry Junkyard: Geometric Topology Numerous links in the Geometry Junkyard. http://www.ics.uci.edu/~eppstein/junkyard/topo.html

Geometric Topology This area of mathematics is about the assignment of geometric structures to topological spaces, so that they "look like" geometric spaces. For instance, compact two dimensional surfaces can have a local geometry based on the sphere (the sphere itself, and the projective plane), based on the Euclidean plane (the torus and the Klein bottle), or based on the hyperbolic plane (all other surfaces). Similar questions in three dimensions have more complicated answers; Thurston showed that there are eight possible geometries, and conjectured that all 3-manifolds can be split into pieces having these geometries. Computer solution of these questions by programs like SnapPea has proved very useful in the study of knot theory and other topological problems. Acme Klein Bottle . A topologist's delight, handcrafted in glass. Are most manifolds hyperbolic? From Dave Rusin's known math pages. Bending a soccer ball mathematically . Michael Trott animates morphs between a torus and a double-covered sphere, to illustrate their topological equivalence, together with several related animations. Boy's surface: Wikipedia MathWorld Geometry Center , and an asymmetric animated gif from the Harvard zoo Constructing Boy's surface out of paper and tape.

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