7 votes

Criteria for extending vector field on sphere to ball

View $B^{n}$ as $(S^{n-1}\times[0,1])/(S^{n-1}\times \{1\})$. This means that an extension of a map from $B^{n}$ to somewhere is just an extension to $S^{n-1}\times [0,1]$ which is constant on the ...
HenrikRüping's user avatar
6 votes

Does a coarser topology lead to a non-Hausdorff topological manifold?

Your hypothesis (modifying the topology to produce a non-Hausdorff topological manifold from a Hausdorff one) is impossible, if you assume the non-Hausdorff manifold has dimension equal or less than ...
Willie Wong's user avatar
  • 36.5k
4 votes

Does the group of compactly supported diffeomorphisms have the homotopy type of a CW complex?

I'll explain the claim left in the comments - namely that any paracompact manifold modeled on a strict LF space has CW homotopy type. The notion of an LF space is not completely standard across the ...
Tyrone's user avatar
  • 4,961
4 votes

Projective span of a manifold

With apologies for the self-promotion, my student Baylee Schutte and I now have a paper on this topic called Projective span of Wall manifolds. We calculate the projective span of a family of ...
Mark Grant's user avatar
  • 34.9k
3 votes

How to chart tubes around manifolds with boundary/corners?

From the comments I think the theorem you are looking for is this. I'll be a little fast and loose just to make it easier to state. Let $M$ be a manifold with corners and $N$ a submanifold, ...
Ryan Budney's user avatar
  • 42.8k

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