The Resource Algebraic topology : an introduction, Rafael Ayala, Eladio Dominquez, Antonio Quintero

Algebraic topology : an introduction, Rafael Ayala, Eladio Dominquez, Antonio Quintero

Label
Algebraic topology : an introduction
Title
Algebraic topology
Title remainder
an introduction
Statement of responsibility
Rafael Ayala, Eladio Dominquez, Antonio Quintero
Creator
Contributor
Subject
Language
eng
Cataloging source
YDXCP
Dewey number
514.2
Illustrations
illustrations
Index
index present
LC call number
QA612
LC item number
.A93 2012
Literary form
non fiction
Nature of contents
bibliography
Label
Algebraic topology : an introduction, Rafael Ayala, Eladio Dominquez, Antonio Quintero
Publication
Bibliography note
Includes bibliographical references (p. 354-360) and index
http://library.link/vocab/branchCode
  • zbnus
  • mel
Contents
  • Machine generated contents note: 1.1.Basic notions of general topology -- 1.2.Quotient and attaching spaces -- 1.3.Surfaces and manifolds -- 1.4.Topological groups and group actions -- 1.5.Some notions of homotopy theory -- 1E.Exercises -- 1P.Problems -- 2.1.Simplices and simplicial complexes -- 2.2.Barycentric subdivisions -- 2.3.The topology of a polyhedron -- 2.4.The product triangulation -- 2.5.Simplicial maps and simplicial approximations -- 2E.Exercises -- 2P.Problems -- 3.1.Abstract complexes -- 3.2.Triangulations of quotient spaces -- 3.2A.Triangulations of pushouts of polyhedra -- 3.2B.Triangulations of orbit spaces -- 3.3.OW-complexes -- 3E.Exercises -- 3P.Problems -- 4.1.Modules -- 4.2.Exact sequences of modules -- 4.3.Chain complexes and homology -- 4.4.Cochain complexes and cohomology -- 4.5.More homological algebra -- 4E.Exercises -- 4P.Problems -- 5.1.Oriented simplicial homology -- 5.2.The computability of the simplicial homology. Block homology --
  • Contents note continued: 5.3.Ordered simplicial homology. Equivalence with the oriented simplicial homology -- 5.4.Simplicial homology with coefficients -- 5.5.Simplicial homology and barycentric subdivisions. Homotopy invariance of simplicial homology -- 5.6.Simplicial cohomology -- 5.7.Cup-product and cap-product -- 5E.Exercises -- 5P.Problems -- 6.1.Pseudomanifolds and n-polyhedra. Orientation -- 6.2.Basic geometrical constructions -- 6.3.Desingularizing n-polyhedra to pseudomanifolds -- 6.4.Orientation and (co)homology -- 6E.Exercises -- 6P.Problems -- 7.1.Dual cells -- 7.2.Homology manifolds -- 7.3.Poincare-́Alexander Duality -- 7.4.Duality and cap- and cup-products -- 7.5.Lefschetz Duality -- 7E.Exercises -- 7P.Problems -- 8.1.Singular M-bordism theory -- 8.2.Basic properties of the singular M-bordism -- 8.2A.Exactness of the Mayer-Vietoris sequence (algebraic version) -- 8.2B.Exactness of the Mayer-Vietoris sequence (geometrical version) -- 8.3.Unoriented bordism --
  • Contents note continued: 8.4.The bordism groups of the product of a space with a sphere -- 8.5.The exterior product in bordism theory -- 8E.Exercises -- 8P.Problems -- 9.1.The equivalence between pseudobordism and simplicial homology -- 9.2.Unoriented pseudobordism and simplicial homology with coefficients in Z2 -- 9.3.Some invariance properties -- 9.4.Pseudocobordism and simplicial cohomology -- 9E.Exercises -- 9P.Problems -- 10.1.Singular (co)homology -- 10.2.The equivalence between singular homology and pseudobordism -- 10.2A.Cohomology and differential geometry -- 10.3.(Co)homology theories. The Eilenberg-Steenrod axioms -- 10E.Exercises -- 10P.Problems -- 11.1.The Brouwer fixed-point theorem -- 11.1A.The extension of Brouwer's theorem to infinite dimensions -- 11.2.Trace of an endomorphism. The Hopi trace theorem -- 11.3.The Lefschetz-Hopf fixed-point theorem -- 11E.Exercises -- 11P.Problems -- 12.1.The Jordan-Brouwer theorem -- 12.2.The Borsuk Separation Criterion --
  • Contents note continued: 12E.Exercises -- 12P.Problems -- 13.1.Degree of maps between spheres -- 13.2.The degree of maps between euclidean open sets -- 13.3.The degree of differentiable maps -- 13E.Exercises -- 13P.Problems -- 14.1.Homotopy groups -- 14.2.The Hurewicz homomorphism -- 14E.Exercises -- 14P.Problems -- 15.1.Lens spaces -- 15.2.(Co)homology and homotopy of lens spaces -- 15.3.Homotopy classification of lens spaces
Control code
000049051778
Dimensions
25 cm
Extent
xv, 369 p.
Isbn
9781842657362
Other physical details
ill.
http://library.link/vocab/recordID
.b26471061
System control number
  • (OCoLC)780036609
  • mb26471061

Library Locations

    • Deakin University Library - Melbourne Burwood CampusBorrow it
      221 Burwood Highway, Burwood, Victoria, 3125, AU
      -37.846510 145.115099
    • Deakin University Library - Geelong Waurn Ponds CampusBorrow it
      75 Pigdons Road, Waurn Ponds, Victoria, 3216, AU
      -38.195656 144.304955
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