Winding around : the winding number in topology, geometry, and analysis / John Roe.
Material type:
TextSeries: Student mathematical library ; volume 76Publication details: India American Mathematical Society 2015Description: xiii, 269 pages : illustrations ; 22 cmISBN: - 9781470438463
- 9781470421984 (alk. paper)
- 1470421984 (alk. paper)
- 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
- 515 ROE-J 23
- QA299.8 .R64 2015
- 55M25 | 57M05 | 47A53 | 58A10 | 55N15
| Item type | Current library | Collection | Shelving location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|---|---|
Books
|
BITS Pilani Hyderabad | 510 | General Stack (For lending) | 515 ROE-J (Browse shelf(Opens below)) | Available | 36744 |
"Mathematics advanced study semesters."
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.
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