Elements of algebraic topology (eBook, 2018) [WorldCat.org]
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Elements of algebraic topology
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Elements of algebraic topology

Author: James R Munkres
Publisher: Boca Raton : CRC Press, 2018.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners.
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: James R Munkres
ISBN: 9780429493911 0429493916
OCLC Number: 1028553042
Notes: "The Advanced book program."
Description: 1 online resource
Contents: Cover; Title Page; Copyright Page; Table of Contents; Preface; Chapter 1: Homology Groups of a Simplicial Complex; Â1 Simplices; Â2 Simplicial Complexes and Simplicial Maps; Â3 Abstract Simplicial Complexes; Â4 Review of Abelian Groups; Â5 Homology Groups; Â6 Homology Groups of Surfaces; Â7 Zero-dimensional Homology; Â8 The Homology of a Cone; Â9 Relative Homology; *Â10 Homology with Arbitrary Coefficients; *Â11 The Computability of Homology Groups; Â12 Homomorphisms Induced by Simplicial Maps; Â13 Chain Complexes and Acyclic Carriers Chapter 2: Topological Invariance of the Homology GroupsÂ14 Simplicial Approximations; Â15 Barycentric Subdivision; Â16 The Simplicial Approximation Theorem;  17 The Algebra of Subdivision; Â18 Topological Invariance of the Homology Groups; Â19 Homomorphisms Induced by Homotopic Maps; Â20 Review of Quotient Spaces; *Â21 Application: Maps of Spheres; *Â22 Application: The Lefschetz Fixed-point Theorem; Chapter 3: Relative Homology and the Eilenberg-Steenrod Axioms; Â23 The Exact Homology Sequence; Â24 The Zig-zag Lemma; Â25 Mayer-Vietoris Sequences Â26 The Eilenberg-Steenrod AxiomsÂ27 The Axioms for Simplicial Theory; *Â28 Categories and Functors; Chapter 4: Singular Homology Theory; Â29 The Singular Homology Groups; Â30 The Axioms for Singular Theory; Â31 Excision in Singular Homology; *Â32 Acyclic Models; Â33 Mayer-Vietoris Sequences; Â34 The Isomorphism Between Simplicial and Singular Homology; *Â35 Application: Local Homology Groups and Manifolds; *Â36 Application: The Jordan Curve Theorem; Â37 More on Quotient Spaces; Â38 CW Complexes; Â39 The Homology of CW Complexes *Â40 Application: Projective Spaces and Lens SpacesChapter 5: Cohomology; Â41 The Horn Functor; Â42 Simplicial Cohomology Groups; Â43 Relative Cohomology; Â44 Cohomology Theory; Â45 The Cohomology of Free Chain Complexes; *Â46 Chain Equivalences in Free Chain Complexes; Â47 The Cohomology of CW Complexes; Â48 Cup Products; Â49 Cohomology Rings of Surfaces; Chapter 6: Homology with Coefficients; Â50 Tensor Products; Â51 Homology with Arbitrary Coefficients; Chapter 7: Homological Algebra; Â52 The Ext Functor; Â53 The Universal Coefficient Theorem for Cohomology Â54 Torsion ProductsÂ55 The Universal Coefficient Theorem for Homology; *Â56 Other Universal Coefficient Theorems; Â57 Tensor Products of Chain Complexes; Â58 The Künneth Theorem; Â59 The Eilenberg-Zilber Theorem; *Â60 The Künneth Theorem for Cohomology; *Â61 Application: The Cohomology Ring of a Product Space; Chapter 8: Duality in Manifolds; Â62 The Join of Two Complexes; Â63 Homology Manifolds; Â64 The Dual Block Complex; Â65 Poincaré Duality; Â66 Cap Products; Â67 A Second Proof of Poincaré Duality; *Â68 Application: Cohomology Rings of Manifolds
Responsibility: James R. Munkres.

Abstract:

Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners.

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