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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.
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
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
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