Winding around : the winding number in topology, geometry, and analysis

Winding around the winding number in topology, geometry, and analysis

Prelude: Love, Hate, and ExponentialsPaths and Homotopies -- The Winding Number -- Topology of the Plane -- Integrals and the Winding Number -- Vector Fields and the Rotation Number -- The Winding Number in Functional Analysis -- Coverings and the Fundamental Group -- Coda: The Bott Periodicity Theo...

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1. Verfasser: Roe, John (VerfasserIn)
Format: UnknownFormat
Sprache:eng
Veröffentlicht: Providence, Rhode Island American Mathematical Society, Mathematics Advanced Study Semesters 2015
Schriftenreihe:Student mathematical library volume 76
Schlagworte:
Mathematical analysis > Foundations > Associative law (Mathematics) > Symmetric functions > Commutative law (Mathematics) > Algebraic topology -- Classical topics -- Degree, winding number > Manifolds and cell complexes -- Low-dimensional topology -- Fundamental group, presentations, free differential calculus > Operator theory -- General theory of linear operators -- (Semi-) Fredholm operators > index theories > Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Differential forms > Algebraic topology -- Homology and cohomology theories -- $K$-theory > Lehrbuch > Analysis > Assoziativgesetz > Symmetrische Funktion > Kommutativgesetz > Algebraische Topologie > Differentialgeometrie > Windungszahl
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Zusammenfassung:Prelude: Love, Hate, and ExponentialsPaths and Homotopies -- The Winding Number -- Topology of the Plane -- Integrals and the Winding Number -- Vector Fields and the Rotation Number -- The Winding Number in Functional Analysis -- Coverings and the Fundamental Group -- Coda: The Bott Periodicity Theorem -- Appendix A: Linear Algebra -- Appendix B: Metric Spaces -- Appendix C: Extension and Approximation Theorems -- Appendix D: Measure Zero -- Appendix E: Calculus on Normed Spaces -- Appendix F: Hilbert Space -- Appendix G: Groups and Graphs.
Prelude: Love, Hate, and Exponentials -- Paths and Homotopies -- The Winding Number -- Topology of the Plane -- Integrals and the Winding Number -- Vector Fields and the Rotation Number -- The Winding Number in Functional Analysis -- Coverings and the Fundamental Group -- Coda: The Bott Periodicity Theorem -- Appendix A: Linear Algebra -- Appendix B: Metric Spaces -- Appendix C: Extension and Approximation Theorems -- Appendix D: Measure Zero -- Appendix E: Calculus on Normed Spaces -- Appendix F: Hilbert Space -- Appendix G: Groups and Graphs
Beschreibung:Includes bibliographical references and index
Beschreibung:xiii, 269 Seiten
Illustrationen, Diagramme
ISBN:9781470421984
978-1-4704-2198-4
1470421984
1-4704-2198-4