Algebraic Topology: An Introduction by Rafael Ayala, Rafael Ayala Gómez, Eladio Dominguez, Antonio Quintero ISBN 9781842657362, 1842657364 instant download

Algebraic Topology: An Introduction by Rafael Ayala, Rafael Ayala Gómez, Eladio Dominguez, Antonio Quintero ISBN 9781842657362, 1842657364 instant download

Beginning with the combinatorial definition of simplicial (co)homology and its main properties (including duality for homology manifolds), this book is vital to any beginner new to the subject of topology, or for those wishing to refresh their knowledge as it dives into the topic supported by a wealth of exercises and problems. The classical applications of (co) homology theory are included, the geometrical facet of (co) homology via bordism theory is sketched and it is demonstrated the corresponding theory for pseudo-manifolds coincides with the homology obtained from the singular chain complex. The book also contains a geometric approach to the Hurewicz theorem relating homology and homotropy, before the final 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.
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 The Hurewicz Homomorphism
• The homotopy classification of lens spaces
• Appendices
• Bibliography
• Index.