TY  - BOOK
AU  - Roe,John
TI  - Winding around: the winding number in topology, geometry, and analysis 
T2  - Student mathematical library
SN  - 9781470438463
AV  - QA299.8 .R64 2015
U1  - 515 ROE-J 23
PY  - 2015///
CY  - India
PB  - American Mathematical Society
KW  - Mathematical analysis
KW  - Foundations
KW  - Associative law (Mathematics)
KW  - Symmetric functions
KW  - Commutative law (Mathematics)
KW  - Algebraic topology -- Classical topics -- Degree, winding number
KW  - msc
KW  - Manifolds and cell complexes -- Low-dimensional topology -- Fundamental group, presentations, free differential calculus
KW  - Operator theory -- General theory of linear operators -- (Semi-) Fredholm operators; index theories
KW  - Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Differential forms
KW  - Algebraic topology -- Homology and cohomology theories -- $K$-theory
N1  - "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
ER  -