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Results tagged with manifolds
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user 32022
A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
11
votes
Accepted
Mapping class groups in high dimension
Let me assume that M is at least 5-dimensional.
Sullivan's proof only uses surgery theory and properties of O(n) that also hold for Top(n), so the answer to your first question is yes.
Regarding your …
- 2,974
26
votes
2
answers
2k
views
Are there geometrically formal manifolds, which are not rationally elliptic?
For compact manifolds, this is clearly equivalent to having finite dimensional rational homotopy. … There are examples of rationally elliptic compact simply-connected manifolds, which are not geometrically formal. …
- 2,974
14
votes
2
answers
2k
views
Reference Request: Compact manifolds with boundary have the homotopy type of a CW-complex
Let $M$ be a compact manifold (possibly non-smooth) manifold with boundary $\partial M$.
Is the inclusion $\partial M\hookrightarrow M$ homotopy equivalent to the inclusion of a subcomplex into a CW- …
- 2,974