Re: diffeomorphism group of R^n
- From: Christoph Wockel <christoph.wockel@xxxxxxx>
- Date: Mon, 14 Jan 2008 02:37:35 -0800 (PST)
On Jan 12, 4:33 pm, "Phillip E. Parker" <p...@xxxxxxxxxxxxxxxx> wrote:
And to all: How does the toplogy used by Stewart compare with those of Kriegl-Michor and of Gloeckner?
The topology used/constructed by Gloeckner has the compactly supported
diffeos as the identity component. In particular, O(n) intersects the
identity component trivially (seems some kind of strange to me). So
this topology is finer than the topology of compact convergence used
by Stewart.
It looks as if the last (Gloeckner) is the most suitable for my purposes, but I'd like it to have the fibrations of Stewart as well. For one thing, he's the only one I've noticed so far that considers the isotropy subgroup of the natural action on R^n (those fixing 0 in R^n).
And if anyone knows anything about the algebraic structure of these groups, please tell me.
The identity component of diffeomorphism groups tend to be simple. For
the compact case this is
D.B.A. Epstein, The simplicity of certain groups of homeomorphisms,
Compositio Math. 22 1970 165--173
S. Haller, J. Teichmann, Smooth perfectness through decomposition of
diffeomorphisms into fiber preserving ones, Ann. Global Anal. Geom.
23 (2003), no. 1, 53--63.
I think that the result of Epstein could be used in the R^n case for
the topology that Gloeckner uses as well.
Christoph Wockel
.
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- From: Phillip E. Parker
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