the winding number in topology, geometry, and analysis /
John Roe
xiii, 269 pages :
illustrations ;
22 cm
Student mathematical library ;
volume 76
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