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Results tagged with differential-topology
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user 1822
The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
40
votes
Accepted
Do "surjective" degree zero maps exist?
It is a theorem of H. Hopf that a map between connected, closed, orientable n-manifolds of degree 0 is homotopic to a map that misses a point, when n > 2. See D. B. A. Epstein, The degree of a map. Pr …
- 3,376
4
votes
Accepted
A reference for an equivariant Morse Lemma
Check Wasserman, Arthur G. Equivariant differential topology. Topology 8 1969 127--150. MR0250324 (40 #3563). In particular see Lemma 4.1 for an equivariant Morse lemma.
- 3,376
3
votes
Accepted
Under what conditions are two orientation-reversing involutions of a compact surface equival...
Two orientation-reversing involutions of a given closed orientable surface are equivalent if and only they have the same number of fixed point circles and have the same orientation character, in the s …
- 3,376