Algebraic topology : an introduction / Rafael Ayala, Eladio Dominguez and Antonio Quintero.

By:

Ayala, Rafael

Contributor(s):

Publication details: Oxford : Alpha Science, c2012.Description: xv, 369 p. : illustrations ; 25 cmISBN:

9781842657362

Subject(s):

Algebraic topology

DDC classification:

23 Ay973 514.2

Contents:

1. Preliminaries of topology -- 2. Simplicial complexes -- 3. Extending the definition of a simplicial complex -- 4. Notions of homological algebra -- 5. Simplicial homology -- 6. Pseudomanifolds and n-polyhedra -- 7. Duality in manifolds -- 8. Singular bordism -- 9. Pseudobordism and simplicial homology -- 10. Singular (Co)homology -- 11. The fixed-point theorems of Brouwer and Lefschetz-Hopf -- 12. The Jordan-Brouwer separation therorem -- 13. A glimpse at the theory of degree -- 14. Homology and homotopy: the Hurewicz homomorphism -- 15. The homology classification of lens spaces-- Appendices A-K-- Bibliography-- Index.

Summary: Starts with the combinatorial definition of simplicial (co) homology and its main properties (including duality for homology manifolds). This book presents a geometric approach to the Hurewicz theorem relating homology and homotopy.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
Books	ISI Library, Kolkata	514.2 Ay973 (Browse shelf(Opens below))	Available		135474

Total holds: 0

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Previous	514.2 An546 Boundedly controlled topology	514.2 An597 Differential algebras in topology	514.2 An634 Concordance-Homotopy groups of geometric automorphism groups	514.2 Ay973 Algebraic topology : an introduction /	514.2 B242 Algebraic topology	514.2 B242 Algebraic topology: new trends in localization and periodicity	514.2 B242(3) Algebraic topology homotopy and group cohomology	Next

Includes bibliographical references and index.

1. Preliminaries of topology --
2. Simplicial complexes --
3. Extending the definition of a simplicial complex --
4. Notions of homological algebra --
5. Simplicial homology --
6. Pseudomanifolds and n-polyhedra --
7. Duality in manifolds --
8. Singular bordism --
9. Pseudobordism and simplicial homology --
10. Singular (Co)homology --
11. The fixed-point theorems of Brouwer and Lefschetz-Hopf --
12. The Jordan-Brouwer separation therorem --
13. A glimpse at the theory of degree --
14. Homology and homotopy: the Hurewicz homomorphism --
15. The homology classification of lens spaces--

Appendices A-K--
Bibliography--
Index.

Starts with the combinatorial definition of simplicial (co) homology and its main properties (including duality for homology manifolds). This book presents a geometric approach to the Hurewicz theorem relating homology and homotopy.

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