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Results tagged with smooth-manifolds
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user 2039
Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].
14
votes
Accepted
Does $\mathfrak{N}_4$ contain at least four distinct elements?
Thom proved that the unoriented bordism is a polynomial ring over $\mathbb{F}_2$ generated by elements $x_i$ with $i$ running over all numbers not of the form $2^k-1$. Thus, $\mathfrak{N}_4 = \mathbb{ …
- 12.1k
4
votes
Accepted
Do trivial homotopy groups imply existence of boundary preserving homotopies?
Let me first talk only about continuous maps. Your question becomes equivalent to asking whether every map from $\partial (M\times I) \to N$ (for $I$ the interval) can be extended to $M\times I$. This …
- 12.1k
4
votes
Easier ways to compute homology/cohomology by adding extra structure
Given a Morse function on a Riemannian smooth manifold, you obtain (under mild conditions) a chain complex computing its homology, the Morse complex. Its generators are the critical points and differe …
- 12.1k