Re: diffeomorphism group of R^n

Linus Kramer <lkram_01@xxxxxxxxxxxxxxxxxxxx> writes:

phil@xxxxxxxxxxxxxxxx wrote:
Where can I learn what is known about the diffeomorphism group of real
n-space?

From what I can tell, this info seems to be scattered about the
journals (and presumably lecture notes). Not being an expert in this
area, I seek a single source such as a review (precis, summary, etc.)
to get me into the relevant literature.

I need the information for some research I am doing into nonlinear
Ehresmann connections.


The diffeomorphism group of R^n deformation retracts onto the
orthogonal group, so in terms of homotopy theory, it looks like
O(n).

But of course its structure as a discrete group (even as a topological
group, through more discerning lenses than that of homotopy theory) is
very unlike that of O(n). For instance, Diff(R^n) is k-transitive for
every finite k (if n > 1). I wouldn't know a nonlinear Ehresmann
connection if it bit me, but I strongly suspect it would care about
structure at a level more subtle than homotopy. (If it wouldn't, it
would be welcome to bite me.)

Lee Rudolph

.