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Results tagged with at.algebraic-topology
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user 94671
Homotopy theory, homological algebra, algebraic treatments of manifolds.
7
votes
4
answers
767
views
Topological invariance of Stiefel-Whitney classes for open smooth manifolds
It is well known that Stiefel-Whitney classes are homotopy invariant for closed smooth manifolds. But in the case of open manifolds even $w_1$ is not a homotopy invariant (take just open cylinder and …
- 141
4
votes
Topological invariance of Stiefel-Whitney classes for open smooth manifolds
The topological invariance of Stiefel-Whitney classes of smoothable manifolds is just a classic theorem of Thom, written in one of his most famous papers. It was pointed out to me by Alexander A. Gaif …
- 141
3
votes
Topological invariance of Stiefel-Whitney classes for open smooth manifolds
Here is the proof of the Conjecture 1. The idea of the proof came from the upper answer by Danny Ruberman and by private communication with Semen Podkorytov. I am very grateful to them!
To prove th …
- 141