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Results tagged with differential-topology
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user 2039
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”.
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
12
votes
Conceptual proof of classification of surfaces?
This is more an extended comment than an answer to the question. The first thing to note is that there are different strenghts of the classification theorem for surfaces. Of course, there are the diff …
- 12.1k