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Results tagged with lie-groups
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user 184
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
18
votes
Accepted
What is the classifying space of "G-bundles with connections"
There is a stupid answer which is equivalence classes of G-bundles with connection on M are the same as homotopy classes of maps $M \to BG$. That is as long as two G-bundles with connection are consid …
- 27.5k
5
votes
Accepted
Can there exist two non-equivalent equivariant actions of a group on vector bundle?
Maybe I am miss understanding the question, but it seems the answer is yes.
Take your favorite G-space, mine is $S^1$ with the $\mathbb{Z}/2$-action "flip". Then consider the trivial vector bundles $ …
- 27.5k
2
votes
1
answer
197
views
Polytopes related to the conjugation action of a Lie group on multiple copies of itself?
Let G be a finite dimensional real Lie group. As I understand it, the quotient space of G acting on itself by conjugation is a well studied polytope which can be identified with the fundamental alcove …
- 44.7k