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Author Roe, John, 1959-
Title Winding around : [electronic resource] the winding number in topology, geometry, and analysis / John Roe
Imprint Providence, Rhode Island : American Mathematical Society, [2015]
©2015
book jacket
Descript 1 online resource (xiii, 269 pages : illustrations)
text rdacontent
unmediated rdamedia
volume rdacarrier
Series The Student Mathematical Library, 1520-9121 (print); v. 76
Note "Mathematics advanced study semesters."
Includes bibliographical references and index
Chapter 1. Prelude: Love, hate, and exponentials Chapter 2. Paths and homotopies Chapter 3. The winding number Chapter 4. Topology of the plane Chapter 5. Integrals and the winding number Chapter 6. Vector fields and the rotation number Chapter 7. The winding number in functional analysis Chapter 8. Coverings and the fundamental group Chapter 9. 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
Access is restricted to licensed institutions
Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2015
Mode of access : World Wide Web
Description based on print version record
Link Print version: Roe, John, 1959- Winding around : (DLC) 2015019246 1520-9121 9781470421984
Subject Mathematical analysis -- Foundations
Associative law (Mathematics)
Symmetric functions
Commutative law (Mathematics)
Algebraic topology -- Classical topics -- Degree, winding number. msc
Manifolds and cell complexes -- Low-dimensional topology -- Fundamental group, presentations, free differential calculus. msc
Operator theory -- General theory of linear operators -- (Semi-) Fredholm operators; index theories. msc
Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Differential forms. msc
Algebraic topology -- Homology and cohomology theories -- $K$-theory. msc
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