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Topology from the Differentiable Viewpoint.
Abstract
Preface1Smooth manifolds and smooth maps1Tangent spaces and derivatives2Regular values7The fundamental theorem of algebra82The theorem of Sard and Brown10Manifolds with boundary12The Brouwer fixed point theorem133Proof of Sard's theorem164The degree modulo 2 of a mapping20Smooth homotopy and smooth isotopy205Oriented manifolds26The Brouwer degree276Vector fields and the Euler number327Framed cobordism the Pontryagin construction42The Hopf theorem508Exercises52AppClassifying 1-manifolds55Bibliography59Index63
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Cited by
Burago, D., Burago, Y., & Ivanov, S. (2001) · Graduate Studies in Mathematics · doi:10.1090/gsm/033 · Cited by 2,598
Robot navigation functions on manifolds with boundary
Koditschek, D. E., & Rimon, E. (1990) · Advances in Applied Mathematics · doi:10.1016/0196-8858(90)90017-s · Cited by 567
Topological polarization singularities in metaphotonics
Liu, W., Liu, W., Shi, L., & Kivshar, Y. (2021) · Nanophotonics · doi:10.1515/nanoph-2020-0654 · Cited by 107
BUENO DE MESQUITA, E., & TYSON, S. A. (2020) · American Political Science Review · doi:10.1017/s0003055419000911 · Cited by 31
Momentum-space spin texture in a topological superconductor
Loder, F., Kampf, A. P., Kopp, T., & Braak, D. (2017) · Physical Review B · doi:10.1103/physrevb.96.024508 · Cited by 16
Metadata
- Authors
- Brown, E. H., & Milnor, J. W.
- Venue
- The American Mathematical Monthly
- Publisher
- JSTOR
- Published
- 1967-04
- Volume
- 74
- Issue
- 4
- Pages
- 461
- ISSN
- 0002-9890 (ISSN-L)
- OpenAlex
- W2041064634
- Cited by
- 1,418
- References
- 0
- FWCI
- 7.86
- Type
- journal article
- Language
- en
- Open access
- closed
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