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Results tagged with differential-topology
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user 22810
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”.
15
votes
0
answers
1k
views
Topological description of a blow up of a manifold along a submanifold
There's a very nice topological description of blow ups of complex manifolds at a point as connected sum with projective space. The following is an attmept to understand whether there's a higher dimen …
- 7,799
8
votes
2
answers
533
views
A map of spaces implementing the Pontryagin Thom collapse map? (collapse maps in families)
Let $M$ be an $n$ dimensional smooth manifold and let $j: M \to \mathbb{R}^{m}$ be an embedding. Associated to this embedding we can form the "collapse map" which is a pointed map from a sphere to the …
- 7,799
5
votes
0
answers
75
views
Bounding the dimension of the euclidean space in which any $n$-manifold embeds "$k$-uniquely...
(The question will be interesting for topological/Pl as well but in order to not be too vague I will restrict the meaning of manifold to smooth manifold without boundary).
I'm interested in the funct …
- 7,799
18
votes
3
answers
4k
views
What is an "Instanton" in classical gauge theory? (to a mathematician)
There's already a question about the same topic but I think its aim is different.
Classical (non-quantum) gauge theory is a completely rigorous mathematical theory. It can be phrased in completely di …
- 7,799
64
votes
1
answer
4k
views
A dictionary of Characteristic classes and obstructions
I apologize in advance as this is not a research level question but rather one which could benefit from expert attention but is potentially useful mainly to novice mathematicians.
In an effort to ge …
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