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         Algebraic Topology:     more books (100)
  1. A First Course in Topology: Continuity and Dimension (Student Mathematical Library) by John McCleary, 2006-04-07
  2. Applications of Algebraic Topology: Graphs and Networks, The Picard-Lefschetz Theory and Feynman Integrals (Applied Mathematical Sciences 16) (Volume 0) by S. Lefschetz, 1975-05-13
  3. Fundamental Algebraic Geometry (Mathematical Surveys and Monographs) by Barbara Fantechi, Lothar Gottsche, et all 2006-12-10
  4. Topological Methods in Algebraic Geometry (Classics in Mathematics) by Friedrich Hirzebruch, 1995-02-24
  5. Probabilities on Algebraic Structures (Dover Books on Mathematics) by Ulf Grenander, 2008-02-04
  6. Directed Algebraic Topology: Models of Non-Reversible Worlds (New Mathematical Monographs) by Marco Grandis, 2009-10-30
  7. Algorithmic Topology and Classification of 3-Manifolds (Algorithms and Computation in Mathematics) by Sergei Matveev, 2010-11-02
  8. Algebraic K-Theory II. . "Classical" Algebraic K-Theory, and Connections with Arithmetic.(Lecture Notes in Mathematics 342) (Volume 0) by Hyman Bass, 1973-01-01
  9. Essentials of Topology with Applications (Textbooks in Mathematics) by Steven G. Krantz, 2009-07-28
  10. Fourier-Mukai Transforms in Algebraic Geometry (Oxford Mathematical Monographs) by Daniel Huybrechts, 2006-06-29
  11. Intuitive Combinatorial Topology (Universitext) by V.G. Boltyanskii, V.A. Efremovich, 2010-11-02
  12. Topology, Ergodic Theory, Real Algebraic Geometry
  13. Geometry and Topology of Configuration Spaces by Edward R. Fadell, Sufian Y. Husseini, 2000-12-28
  14. Algebra, Algebraic Topology and their Interactions: Proceedings of a Conference held in Stockholm, Aug. 3 - 13, 1983, and later developments (Lecture Notes in Mathematics)

61. Surgery Bits And Pieces
Assorted articles and minutia concerning Algebraic Surgery, assembled by Andrew Ranicki.
Surgery Bits and Pieces
Biographical material
Surgery, algebraic and otherwise
Books, papers, theses, notes etc.

62. Algebraic Topology Authors/titles Recent Submissions
Title Points fixes des applications compactes dans les espaces ULC math math.AT
Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages
Algebraic Topology
Authors and titles for recent submissions
[ total of 10 entries:
[ showing up to 25 entries per page: fewer more
Fri, 29 Oct 2010
arXiv:1010.6039 (cross-list from math.DG) [ pdf ps other
Title: A pull-back procedure of the Gromoll-Meyer construction Authors: Comments: 11 pages Subjects: Differential Geometry (math.DG) ; Algebraic Topology (math.AT); Geometric Topology (math.GT)
Thu, 28 Oct 2010
arXiv:1010.5635 pdf ps other
Title: The Segal conjecture for topological Hochschild homology of complex cobordism Authors: John Rognes Subjects: Algebraic Topology (math.AT)
arXiv:1010.5633 pdf ps other
Title: The topological Singer construction Authors: John Rognes Subjects: Algebraic Topology (math.AT)
Wed, 27 Oct 2010
arXiv:1010.5269 pdf ps other
Title: The Mayer-Vietoris Property in Differential Cohomology Authors: James Simons Dennis Sullivan Comments: 8 pages Subjects: Algebraic Topology (math.AT)

63. Poincaré Conjecture -- From Wolfram MathWorld
A widely accessible statement of the Poincar Conjecture and its implications, with various links and references for further inquiry.
Applied Mathematics

Calculus and Analysis

Discrete Mathematics
... closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) , where a three-sphere is simply a generalization of the usual sphere to one dimension compact manifold is homotopy -equivalent to the -sphere iff it is homeomorphic to the sphere . The generalized statement reduces to the original conjecture for topology of manifolds Whitehead link ) to his own theorem. The case of the generalized conjecture is trivial, the case is classical (and was known to 19th century mathematicians), (the original conjecture) appears to have been proved by recent work by G. Perelman (although the proof has not yet been fully verified), was proved by Freedman (1982) (for which he was awarded the 1986 Fields medal was demonstrated by Zeeman (1961), was established by Stallings (1962), and was shown by Smale in 1961 (although Smale subsequently extended his proof to include all The Clay Mathematics Institute included the conjecture on its list of $1 million prize problems. In April 2002, M. J. Dunwoody produced a five-page paper that purports to prove the conjecture. However, Dunwoody's manuscript was quickly found to be fundamentally flawed (Weisstein 2002). A much more promising result has been reported by Perelman (2002, 2003; Robinson 2003). Perelman's work appears to establish a more general result known as the Thurston's geometrization conjecture , from which the Poincaré conjecture immediately follows (Weisstein 2003). Mathematicians familiar with Perelman's work describe it as well thought-out and expect that it will be difficult to locate any substantial mistakes (Robinson 2003, Collins 2004). In fact, Collins (2004) goes so far as to state, "everyone expects [that] Perelman's proof is correct."

64. Algebraic Topology
Apr 7, 2009 Algebraic Topology. Download this Document for FreePrintMobileCollectionsReport Rated (1 Rating). Math book Algebraic Topology

65. MAT 539 -- Algebraic Topology
A basic introduction to geometry/topology, such as MAT 530 and MAT 531. Thus prior exposure to basic point set topology, homotopy, fundamental group, covering spaces is assumed
MAT 539
Algebraic Topology Instructor
Sorin Popescu (office: Math 4-119, tel. 632-8358, e-mail Prerequisites A basic introduction to geometry/topology, such as MAT 530 and MAT 531 Textbook Differential forms in algebraic topology , by Raoul Bott and Loring W. Tu, GTM , Springer Verlag 1982.
The guiding principle of the book is to use differential forms and in fact the de Rham theory of differential forms as a prototype of all cohomology thus enabling an easier access to the machineries of algebraic topology in the realm of smooth manifolds. The material is structured around four core sections: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes, and includes also some applications to homotopy theory.
Other recommended texts:
  • Algebraic Topology: A first Course , W. Fulton, GTM , Springer Verlag 1995
  • Topology from the Differentiable Viewpoint , J. Milnor, U. of Virginia Press 1965
  • Algebraic Topology , A. Hatcher (on-line), Cambridge University Press, to appear
  • Characteristic classes , J. Milnor and J. Stasheff, Princeton University Press 1974

66. - Charts
Charts for modules over the odd-primary Steenrod Algebra, by Christian Nassau. In Postscript.
Christian Nassau

67. Algebraic Topology And Distributed Computing A Primer
File Format PDF/Adobe Acrobat Quick View

68. Algebraic Topology Authors/titles "new.AT"
Submissions received from Wed 6 Oct 10 to Thu 7 Oct 10, announced Fri, 8 Oct 10 math math.AT
Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages
Algebraic Topology
New submissions
Submissions received from Wed 27 Oct 10 to Thu 28 Oct 10, announced Fri, 29 Oct 10 [ total of 4 entries:
[ showing up to 2000 entries per page: fewer more
New submissions for Fri, 29 Oct 10
arXiv:1010.6039 pdf ps other
Title: A pull-back procedure of the Gromoll-Meyer construction Authors: Comments: 11 pages Subjects: Differential Geometry (math.DG) ; Algebraic Topology (math.AT); Geometric Topology (math.GT)
Replacements for Fri, 29 Oct 10
arXiv:1005.4878 (replaced) [ pdf ps other
Title: Azumaya Objects in Bicategories Authors: Niles Johnson Comments: 15 pages; minor corrections and clarified exposition in section 6 Subjects: Algebraic Topology (math.AT) ; Category Theory (math.CT); Rings and Algebras (math.RA)
arXiv:1009.3622 (replaced) [ pdf ps other
Title: The homotopy type of toric arrangements Authors: Luca Moci Simona Settepanella Comments: To appear on J. of Pure and Appl. Algebra. 16 pages, 3 pictures Subjects: Algebraic Topology (math.AT)

69. The Hopf Fibration
Notes and images of the Hopf map from S3 to S2.

70. Algebraic Topology
Algebraic Topology . Brief historical introduction . Although algebraic topology can be considered, by and large, as a creation of the 20th century, it has a long prehistory.
Algebraic Topology
Brief historical introduction
Although algebraic topology can be considered, by and large, as a creation of the 20th century, it has a long pre-history. It is generally considered to have its roots in Euler's polyhedron theorem (1752). This is the relation $$ E+F=K+2$$ where $E$ is the number of vertices, $K$ the number of edges, and $F$ the number of faces. In the first half of this century many mathematicians defined homology for more and more extended classes of topological spaces. Thus, for instance singular homology was first defined by Lefschetz in 1933. Finally, in 1945, Eilenberg and Steenrod developed an axiomatic approach to homology. It turned out that within the class of all topological spaces the Eilenberg and Steenrod axioms uniquely characterize singular homology. A parallel development took place in homotopy. Thus, higher homotopy groups were defined by Hurewicz in 1935 and their properties were developed. In the 1950's several new concepts were invented such as cobordism and $K$-theory. The course will be based mainly on Greenberg and Harper's book quoted below.

71. ALGTOP-L, Algebraic Topology Listserv
Includes information on subscribing, archives of past discussions, and links to home pages of algebraic topologists and other related resources.
ALGTOP-L, Algebraic Topology listserv
This listserv began as a discussion group in July 1995, and was converted to an automated moderated listserv in Sept 2007. To join the listserv or use it, go to The primary functions of this listserv are providing information about topology conferences and jobs, and serving as a forum for topics related to algebraic topology. This website also serves as an archive of links to websites related to algebraic topology. As a service for the nonspecialist, we have an

72. J. P. May: A Concise Course In Algebraic Topology
J. P. May, A Concise Course in Algebraic Topology J. P. May A Concise Course in Algebraic Topology 254 pages, 117 line drawings 6 x 9 1999

73. Novikov Conjecture Home Page
An archive of developments concerning the Novikov Conjecture and related problems in Algebraic Topology, General Topology, Geometry, Algebra, and Analysis. Maintained by Jonathan Rosenberg.
Novikov Conjecture Home Page
The intended function of this home page is to keep you up-to-date on the latest developments concerning the Novikov Conjecture and related problems in topology, geometry, algebra, and analysis. Further contributions of all sorts are welcome. Please send them to Jonathan Rosenberg at
Bibliography on the Novikov Conjecture and related topics:
This bibliography is based on the one in "A history and survey of the Novikov Conjecture" by Steve Ferry, Andrew Ranicki, and Jonathan Rosenberg. The original version appeared in volume 1 of "Novikov Conjectures, Index Theorems and Rigidity" (listed below under books) but we will try to update it regularly. To view the dvi file (approx. 80kb), click here . For a tar'ed dvi file (better suited for downloading), click here
Some recent books:

74. Algebraic Topology By Allen Hatcher - Download Here
Algebraic Topology by Allen Hatcher free book at E-Books Directory - download here

75. Algorithms For The Fixed Point Property
A survey of various algorithms used to determine if a given ordered set has the fixed point property, that is, whether it has a fixed point free order-preserving self-map. Algorithms using the methods of Algebraic Topology are compared with other techniques.
Next: Contents
Algorithms for the Fixed Point Property
e-mail: July 29, 1996 Abstract. This survey exhibits various algorithms to decide the question if a given ordered set P has the fixed point property resp. if P has a fixed point free order-preserving self-map.
While a depth-first search algorithm for a fixed point free map is easily written it is also quite inefficient. We discuss a reduction algorithm by Xia which can be used to speed up the search for a fixed point free self map. The ideas used in creating this algorithm show close connections to two problems: the decision whether an ordered set has a fixed point free automorphism and the decision whether a given r -partite graph has an r -clique. The latter two problems are shown to be NP-complete using the work of Goddard, Lubiw and Williamson. The problem to decide whether a given finite ordered set has a fixed point free order-preserving self map has recently been shown to be NP-complete, thus showing that the above close connection is not by accident.
Retraction theorems leading to dismantling algorithms are another approach to the problem. We present the classical dismantling procedure by Rival and extensions by Fofanova, Li, Milner, Rutkowski and the author. These theorems give a polynomial algorithm to decide if an ordered set has the fixed point property for some nice classes of ordered sets (height 1, width 2), and structural insights for other classes (chain-complete ordered sets with no infinite antichains, sets of (interval) dimension 2). The related issue of uniqueness of cores gives an insight into Birkhoff's problem regarding cancellation of exponents. Walker's relational fixed point property for which the analogous problem has a very satisfying solution also is discussed.

76. Topology - Wikibooks, Collection Of Open-content Textbooks
James Munkres, Elements of Algebraic Topology (1984) Joseph J. Rotman, An Introduction to Algebraic Topology (1988) Edwin Spanier, Algebraic Topology (1966)
From Wikibooks, the open-content textbooks collection This page may need to be reviewed for quality. Jump to: navigation search This book contains mathematical formulae that look better rendered as PNG
General Topology is based solely on set theory and concerns itself with structures of sets. It is at its core a generalization of the concept of distance, though this will not be immediately apparent for the novice student. Topology generalizes many distance-related concepts, such as continuity, compactness, and convergence. For an overview of the subject of topology, please see the Wikipedia entry

77. Algebraic Topology | Define Algebraic Topology At
–noun Mathematics . the branch of mathematics that deals with the application of algebraic methods to topology, esp. the study of homology and homotopy. topology?qsrc=2446

78. Algebraic K-Theory, Linear Algebraic Groups And Related Structures
TMR Network Project. Network Coordinator Ulf Rehmann, Bielefeld AG/

79. Greenberg M.j. Harper J.r. Algebraic Topology. A First Course Download Links
Download links for greenberg mj harper jr algebraic topology. a first course. FileCatch Search for Shared Files. m.j. harper j.r. algebraic topology. a fir

80. 19: K-theory
Encyclopedic reference for K-Theory in Dave Rusin s Mathematical Atlas. Includes a brief history along with various links to textbooks, reference works, and tutorials on the subject.
Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields
POINTERS: Texts Software Web links Selected topics here
19: K-theory
K-theory is an interesting blend of algebra and geometry. Originally defined for (vector bundles over) topological spaces it is now also defined for (modules over) rings, giving extra algebraic information about those objects.
Read Atiyah's, "K-Theory Past and Present" at here
Applications and related fields
Most of the geometric K-theory is treated with Algebraic Topology See also 16E20, 18F25
  • Grothendieck groups and K_0, see also 13D15, 18F30
  • Whitehead groups and K_1
  • Steinberg groups and K_2
  • Higher algebraic K-theory
  • K-theory in geometry
  • K-theory in number theory, see also 11R70, 11S70
  • K-theory of forms, see also 11EXX
  • Obstructions from topology
  • K-theory and operator algebras See mainly 46L80, and also 46M20
  • Topological K-theory, see also 55N15, 55R50, 55S25
  • Miscellaneous applications of K-theory
K-Theory is the smallest of the 61 active areas of the MSC scheme: only 515 papers with primary classification 19-XX during 1980-1997. But the area 19-XX was only available as a primary classification for Math Reviews papers starting with MR96; hence the count above is an undercount of the true size of the field. (Even granting this, however, K-theory is a fairly small field.) Browse all (old) classifications for this area at the AMS.

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