Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose $M$ is a smooth and metrizable manifold. Then $\operatorname{Isom}{(M)}$ can be given the structure of a Lie group, so that the action of $\operatorname{Isom}{(M)}$ on $M$ is still smooth.

I found that as a sidenote somewhere. I really would like to see a prove of the above. So if somebody happens to know an online (free accessible) source, please tell me. I know $\operatorname{Isom}{(M)}$ is locally compact w.r.t. the compact-open topology. Is this also the topology of the Lie-Group?

share|cite|improve this question
Certainly this doesn't even come close to answering the question, but you should think about the fact that the Lie algebra will be $\Gamma(TM)$, the vector fields on $M$ (if you haven't already). – Aaron Mazel-Gee May 1 '12 at 14:47

How about this, this or this?

share|cite|improve this answer
thank you very much – fk44 May 3 '12 at 16:12
@fk44: I should mention that those links were obtained by a very simple Google search (I certainly have no expertise in this field). It is always a good idea to do a thorough search before asking a question on this and similar sites. – Martin Wanvik May 3 '12 at 16:30

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.