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

By: Contributor(s): Publication details: Oxford : Alpha Science, c2012.Description: xv, 369 p. : illustrations ; 25 cmISBN:
  • 9781842657362
Subject(s): 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

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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