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6 votes
2 answers
379 views

About Lie group $G$ has this escape property?

Every Lie group $G$ has the following escape property: For every $x \ne e$ in a sufficiently small neighborhood $U$ of the identity $e$ in $G$, there is a integer $n$ such that $x^n$ is not in $U$. ...
free's user avatar
  • 71
3 votes
1 answer
454 views

Principal bundles from a fibration of homogeneous spaces

Let $G$ be a compact (Lie) group, and $H \subseteq H'$ two compact (Lie) subgroups. It is clear that we have an obvious surjective map of homogeneous spaces $$ G/H \twoheadrightarrow G/H'. $$ Will it ...
Spyros Olympopolous's user avatar
3 votes
0 answers
58 views

Criteria for density of subgroup of diffeomorphism group

Let $C^{\infty,\star}(\mathbb{R}^d)$ denote the non-commutative topological group of smooth diffeomorphisms from $\mathbb{R}^d$ to itself with $\circ$ as multiplication and let $\emptyset\subset X\...
ABIM's user avatar
  • 5,405
3 votes
0 answers
64 views

Metrically homogeneous spaces as inverse limits

Let $(X,d)$ be a locally compact, separable, connected and $\sigma$-compact metric space such that the group of isometries $G$ acts transitively on $X$. The question is the following: Is $X$ ...
user44172's user avatar
  • 541
2 votes
1 answer
571 views

On homeomorphic compact connected topological groups

I wish to thank Professor Claudio Gorodski for his very helpful answers to my question on the webcite: If compact connected Lie groups are homeomorphic as topological space, are they isomorphic as Lie ...
sife's user avatar
  • 491