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Results tagged with differential-topology
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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”.
63
votes
0
answers
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Are there periodicity phenomena in manifold topology with odd period?
The study of $n$-manifolds has some well-known periodicities in $n$ with period a power of $2$:
$n \bmod 2$ is important. Poincaré duality implies that odd-dimensional compact oriented manifolds ha …
30
votes
1
answer
2k
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Which of the proofs of the fundamental theorem of algebra can actually produce bounds on whe...
One of the old classic MO questions is a big-list of proofs of the fundamental theorem of algebra. Here is a second big-list question about this big list:
Which of the FTA proofs can, even in prin …
- 26.5k
32
votes
2
answers
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When is there a submersion from a sphere into a sphere?
(First posted on math.SE, with no answers.)
That is:
For which positive integers $n, k \ge 1$ does there exist a submersion $S^{n+k} \to S^k$?
The discussion at this math.SE question has narro …
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- 1