Topology from the differentiable viewpoint
Material type: TextSeries: Princeton landmarks in mathematics and physicsPublication details: Princeton, N.J. : Princeton University Press, ©1997Description: ix, 64 pages : illustrationsISBN: 9780691048338; 0691048339 Subject(s): Differential topologyDDC classification: 514.72Item type | Current library | Collection | Call number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|
Reference Books | Main Library Reference | Reference | 514.72 MIL (Browse shelf(Opens below)) | Available | 009748 |
Browsing Main Library shelves, Shelving location: Reference, Collection: Reference Close shelf browser (Hides shelf browser)
514.3 STE Counterexamples in Topology | 514.3 SUT Introduction to Metric and Topological Spaces | 514.72 BRO Introduction to Differential Topology | 514.72 MIL Topology from the differentiable viewpoint | 514.72 SAU An introduction to catastrophe theory | 515 ABB Teach Yourself: Calculus | 515 ALI Principles of Real Analysis |
Includes Index
Preface --
1. Smooth manifolds and smooth maps --
Tangent spaces and derivatives --
Regular values --
The fundamental theorem of algebra --
2. The theorem of Sard and Brown --
Manifolds with boundary --
The Brouwer fixed point theorem --
3. Proof of Sard's theorem --
4. The degree modulo 2 of a mapping --
Smooth homotopy and smooth isotopy --
5. Oriented manifolds --
The Brouwer degree --
6. Vector fields and the Euler number --
7. Framed cobordism the Pontryagin construction --
The Hopf theorem --
8. Exercises --
Provides a clear introduction to one of the important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, this book goes on to examine tangent spaces, oriented manifolds, and vector fields. It discusses concepts such as homotopy, the index number of a map, and the Pontryagin construction
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