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Results tagged with differential-topology
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user 6094
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”.
140
votes
7
answers
34k
views
Is the boundary $\partial S$ analogous to a derivative?
Without prethought, I mentioned in class once that the reason the symbol $\partial$
is used to represent the boundary operator in topology is
that its behavior is akin to a derivative.
But after refle …
- 151k
37
votes
2
answers
5k
views
Kervaire invariant: Why dimension 126 especially difficult?
Is there any resource that might help non-experts gains some understanding of why
the Kervaire invariant problem remains open now only in dimension $126$? ($126 =2^7-2=2^{j+1}-2$;
whether $\theta_j=\t …
- 151k
1
vote
0
answers
208
views
Fractional degree of a map?
Is there some natural notion of a fractional degree of a map?
The degree of a map is a generalization of the winding number,
and fractional winding numbers appear in the (mathematical physics)
literat …
- 151k