Algebraic Topology: An Introduction

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9781842657362: Algebraic Topology: An Introduction

ALGEBRAIC TOPOLOGY: An Introduction starts with the combinatorial definition of simplicial (co) homology and its main properties (including duality for homology manifolds). Then the geometrical facet of (co) homology via bordism theory is sketched and it is shown that the corresponding theory for pseudomanifolds coincides with the homology obtained from the singular chain complex. The classical applications of (co) homology theory are included. Degree and fixed-point theory are presented with their extensions to infinite dimensional spaces. The book also contains a geometric approach to the Hurewicz theorem relating homology and homotopy. The last chapter exploits the algebraic invariants introduced in the book to give in detail the homotopical classification of the three-dimensional lens spaces. Each chapter concludes with a generous list of exercises and problems; many of them contain hints for their solution. Some groups of problems introduce a topic not included in the basic core of the book.

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Rafael Ayala.: Departamento de Geometria y Topologia Facultad de Matematicas, Universidad de Sevilla, Apartado, Sevilla Eladio Dominguez.: Departamento de Informatica e lngenieria de Sistemas, Facultad de Ciencias (Edificio de Matematicas) Universidad de Zaragoza, Zaragoza Antonio Quintero.: Departamento de Geometria y Topologia Facultad de Matematicas, Universidad de Sevilla, Apartado, Sevilla

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Rafael Ayala, Eladio Dominguez, Antonio Quintero
Published by Alpha Science International Limited, United Kingdom (2012)
ISBN 10: 1842657364 ISBN 13: 9781842657362
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Book Description Alpha Science International Limited, United Kingdom, 2012. Hardcover. Book Condition: New New. ALGEBRAIC TOPOLOGY: An Introduction starts with the combinatorial definition of simplicial (co) homology and its main properties (including duality for homology manifolds). Then the geometrical facet of (co) homology via bordism theory is sketched and it is shown that the corresponding theory for pseudomanifolds coincides with the homology obtained from the singular chain complex. The classical applications of (co) homology theory are included. Degree and fixed-point theory are presented with their extensions to infinite dimensional spaces. The book also contains a geometric approach to the Hurewicz theorem relating homology and homotopy. The last chapter exploits the algebraic invariants introduced in the book to give in detail the homotopical classification of the three-dimensional lens spaces. Each chapter concludes with a generous list of exercises and problems; many of them contain hints for their solution. Some groups of problems introduce a topic not included in the basic core of the book. Table of Contents: Preface / Introduction / Preliminaries of Topology / Simplicial Complexes / Extending the definition of a Simplicial Complex / Notions of Homological Algebra / Simplicial Homology / Pseudomanifolds and n-polyhedra / Duality in manifolds / Singular Bordism / Pseudobordism and Simplicial Homology / Singular (Co)homology / The Fixed-Point Theorems of Brouwer and Lefschetz-Hopf / The Jordan-Brouwer Separation Theorem / A Glimpse at the Theory of Degree / Homology and Homotopy: The Hurewicz Homomorphism / The homotopy classification of lens spaces / Appendices / Bibliography / Index. 386pp. Bookseller Inventory # 205647

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Book Description Alpha Science, 2012. Hardcover. Book Condition: Brand New. 369 pages. 9.75x7.50x1.00 inches. In Stock. Bookseller Inventory # zk1842657364

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Rafael Ayala, Eladio Dominguez, Antonio
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Book Description Alpha Science Intl Ltd, 2012. Hardcover. Book Condition: New. Ships with Tracking Number! INTERNATIONAL WORLDWIDE Shipping available. Buy with confidence, excellent customer service!. Bookseller Inventory # 1842657364n

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