Combinatorial Introduction to Topology

Häftad, Engelska, 2003

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Beskrivning

Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

Produktinformation

Utgivningsdatum:2003-03-28
Mått:136 x 214 x 14 mm
Vikt:352 g
Format:Häftad
Språk:Engelska
Serie:Dover Books on MaTHEMA 1.4tics
Antal sidor:320
Förlag:Dover Publications Inc.
ISBN:9780486679662

Utforska kategorier

Innehållsförteckning

Chapter One Basic Concepts1 The Combinatorial Method2 Continuous Transformations in the Plane3 Compactness and Connectedness4 Abstract Point Set TopologyChapter Two Vector Fields5 A Link Between Analysis and Topology6 Sperner's Lemma and the Brouwer Fixed Point Theorem7 Phase Portraits and the Index Lemma8 Winding Numbers9 Isolated Critical Points10 The Poincaré Index Theorem11 Closed Integral Paths12 Further Results and ApplicationsChapter Three Plane Homology and Jordan Curve Theorem13 Polygonal Chains14 The Algebra of Chains on a Grating15 The Boundary Operator16 The Fundamental Lemma17 Alexander's Lemma18 Proof of the Jordan Curve TheoremChapter Four Surfaces19 Examples of Surfaces20 The Combinatorial Definition of a Surface21 The Classification Theorem22 Surfaces with BoundaryChapter Five Homology of Complexes23 Complexes24 Homology Groups of a Complex25 Invariance26 Betti Numbers and the Euler Characteristic27 Map Coloring and Regular Complexes28 Gradient Vector Fields29 Integral Homology30 Torsion and Orientability31 The Poincaré Index Theorem AgainChapter Six Continuous Transformations32 Covering Spaces33 Simplicial Transformations34 Invariance Again35 Matrixes36 The Lefschetz Fixed Point Theorem37 Homotopy38 Other HomologiesSupplement Topics in Point Set Topology39 Cryptomorphic Versions of Topology40 A Bouquet of Topological Properties41 Compactness Again42 Compact Metric SpacesHints and Answers for Selected ProblemsSuggestions for Further ReadingBibliographyIndex