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Winding around : the winding number in topology, geometry, and analysis / John Roe.

By: Roe, John, 1959-.
Material type: TextTextSeries: Student mathematical library ; volume 76.Publisher: Providence, Rhode Island : American Mathematical Society, [2015]Copyright date: ©2015Edition: first indian edition.Description: xiii, 269 pages : illustrations ; 22 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781470438463 (pbk.).Subject(s): 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 -- $K$-theoryDDC classification: 515 Other classification: 55M25 | 57M05 | 47A53 | 58A10 | 55N15
Contents:
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.
List(s) this item appears in: 2017-09-22 | easy/fun read
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks 		515 ROE (Browse shelf) Available 10199
Total holds: 0

"Mathematics advanced study semesters."

Gifted by NBHM.

Includes bibliographical references and index.

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.