Reputation
12,982
Next privilege 15,000 Rep.
Protect questions
Badges
4 47 126
Newest
 Announcer
Impact
~408k people reached

6h
answered Extension of functions from geodesically convex compact sets in a Riemannian manifold
6h
comment Linear extension operators for smooth functions: from compact sets to compact sets
@DeaneYang ok, now I have educated myself about the literature surrounding the problem, and I agree I was hasty about brushing off your comment. Thanks for your patience!
May
2
revised Holomorphic contractibility of GL(H)?
Rolled back insertion of LaTeX into question title; this was deliberately omitted on first writing.
May
2
comment Holomorphic contractibility of GL(H)?
I was prompted into asking this by the nice references in this comment: mathoverflow.net/questions/8800/proofs-of-bott-periodicity/…
May
2
comment Holomorphic contractibility of GL(H)?
So for instance, the Eilenberg swindle (one step of the proof) is surely holomorphic, but the rotation into the decomposition needs to be checked etc etc, assuming GL(H) is even a complex manifold.
May
2
comment Holomorphic contractibility of GL(H)?
@MatthiasWendt well, it's got to be more complicated than that, otherwise Kuiper's theorem would be a corollary of the contractibility of S^oo
May
2
comment Holomorphic contractibility of GL(H)?
This is part of the question. Perhaps one wants contractible with respect to the cylinder object using the complex numbers with basepoints 0,1, perhaps. By holomorphic K(Z,2) I mean a natural complex manifold that is homotopically a K(Z,2). Feel free to interpret these definitions as you see fit.
May
2
asked Holomorphic contractibility of GL(H)?
Apr
26
revised When are $k$-sectors of a Lie groupoid a manifold?
Updated answer with link to new arXiv paper
Apr
24
comment Is there any notion of “smoothification” from $\mathbb{R}$-schemes to generalized smooth spaces?
@SaalHardali well, I was even thinking of the Cahiers topos (ncatlab.org/nlab/show/Cahiers+topos), or other well-adapted models of Synthetic Differential Geometry. There are certainly good functors between the category of diffeological spaces and the Cahiers topos.
Apr
24
comment Grothendieck's “List of classes of structures”
@Arrow no! And, looking at the archives, I'm not sure it got through ... :-( Regarding AG's descendants, there are sadly nasty legal issues that have arisen, so I have to take that remark back.
Apr
22
accepted Linear extension operators for smooth functions: from compact sets to compact sets
Apr
21
comment Compact manifolds locally bi-Lipschitz to Euclidean space
Thanks, Benoît! This is just the sort of thing I was after. I'm glad this wasn't entirely trivial.
Apr
21
accepted Compact manifolds locally bi-Lipschitz to Euclidean space
Apr
21
revised Compact manifolds locally bi-Lipschitz to Euclidean space
Clarifying remark
Apr
21
comment Compact manifolds locally bi-Lipschitz to Euclidean space
Thanks all. As I said, two geometers I asked did not think it obvious, which is why I asked here. Perhaps it wasn't clear that I meant bi-Lipschitz in the metric space sense, with the geodesic metric, and not in a pointwise-sense...
Apr
20
comment Compact manifolds locally bi-Lipschitz to Euclidean space
Thanks anyway, for disabusing me of a misconception. I asked a Riemannian geometer and he wasn't sure it was true, which is why I asked!
Apr
20
comment Compact manifolds locally bi-Lipschitz to Euclidean space
@user89334 it's not that simple. See mathoverflow.net/questions/217425/homogeneous-regular-manifolds for the definition.
Apr
20
comment Compact manifolds locally bi-Lipschitz to Euclidean space
@user89334 no, I'm probably missing something. I'm not a metric geometer, so I have no intuition as to if this could be violated in some weird way. I found a reference (Hass&Scott, TAMS 1988) that says "all closed manifolds" are homogeneously regular, so I guess I'm overthinking it.
Apr
20
comment Compact manifolds locally bi-Lipschitz to Euclidean space
I find that this is asking if every compact manifold admits a homogeneously regular Riemannian metric, and Morrey (Annals of Mathematics Second Series, Vol. 49, No. 4 (1948), pp. 807-851, <jstor.org/stable/1969401>) says that "any compact regular Riemannian manifold" has such a metric. Sadly I don't know what he means by 'regular' here.