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Results tagged with lie-groups
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user 23571
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
73
votes
Homotopy groups of Lie groups
The elementary proof that $\pi_1$ is abelian applies more generally to H-spaces (spaces $X$ with a continuous multiplication map $X \times X \to X$ having a 2-sided identity element) without any assum …
- 20k
18
votes
Topological structure of SO(n) as a product
Another line of reasoning: If $SO(n)$ were homeomorphic to the product $S^{n-1}\times SO(n-1)$ then $S^{n-1}$ would be a retract (not deformation retract!) of $SO(n)$, hence $S^{n-1}$ would be an H-sp …
- 20k
8
votes
Accepted
Existence of an isotopy in Riemannian manifold
For the first question, which concerns just the smooth category without reference to metrics, the answer depends on the dimension of $M$. Before explaining this a small clarification is needed. By "a …
- 20k