10,447 reputation
12543
bio website normalesup.org/~cornulier
location
age
visits member for 4 years, 4 months
seen 4 hours ago

12h
comment Generalization of a theorem of Burnside to non-compact groups
Please edit the question to be more precise about the representation you're looking at. Hilbert is still vague: unitary reps? or just continuous?
Jul
30
comment A group topology which commutes with closed subgroups
When G is Hausdorff and not central-by-discrete, there are still some cases where it's abelian-by-discrete which might work, possibly not all.
Jul
30
comment A group topology which commutes with closed subgroups
It holds in a more general setting encompassing both the discrete case and the abelian case, namely when G has an open central subgroup, i.e. when "G is central-by-discrete".
Jul
30
revised Automorphism groups for free groups with action
merged the comment to the text to clarify; added 1 tag
Jul
30
comment The evaluation fibration of a transitive, effective topological group action
If $X$ is a homogeneous real tree not reduced to a line, I think its isometry group $G$ is totally disconnected but $X$ is geodesic, so the action will not be a locally trivial fibre bundle. ($G$ is totally disconnected because its unit component has to act trivially on the boundary, and the action on the boundary is faithful)
Jul
30
revised presentations of subalgebras
edited tags
Jul
30
revised How to associate a proper parabolic subgroup of a real s.s Lie group $G$ to a non-trivial unipotent element in a non uniform lattice in $G$?
edited tags
Jul
29
revised Counting elements with certain word length in abelian groups
edited tags
Jul
29
comment Purely inseparable field extensions of degree p
No idea where this could be written. It sounds quite artificial, so possibly nowhere.
Jul
29
comment Purely inseparable field extensions of degree p
If you want field isomorphism (less natural), replace $K(t,u)$ with $\bigcup_{n\ge 0}K(t^{1/q^n},u)$, where $q$ is coprime to $p$.
Jul
29
comment Purely inseparable field extensions of degree p
Trivial example: $K(t,u^{1/p})\supset K(t,u)\subset K(t^{1/p},u)$, where $p$ is the characteristic of $K$.
Jul
29
comment Purely inseparable field extensions of degree p
You mean isomorphism as $K$-algebras? (i.e. as extensions of $K$?)
Jul
29
comment How to find PDF of ordered random variables?
Translation: PDF: probability density function. CDF: cumulative distribution function
Jul
29
comment Bounded metric spaces with non-surjective self-isometry
Let $t$ be an irrational. Define $X_t=\{e^{int}:n\ge 0\}$; this is a subset of the unit circle. Then the rotation $z\mapsto e^{it}z$ maps $X_t$ into a proper subset of itself; with the Euclidean distance this is a self-isometry of $X_t$. Unlike the Hilbert shift example, it's not a complete metric space.
Jul
28
comment When is the boundary of an open planar set a Jordan curve?
Yeah I was wondering. Actually when I first saw the reference I actually read Igor's post and didn't notice the year and I really thought this was recent (and got surprised a bit that such results could be only done recently).
Jul
28
comment Space of polynomially growing harmonic functions on a Lie group
this paper is here math.uchicago.edu/~shmuel/SAMS2.pdf I couldn't find any definition of being harmonic there (one could imagine several choices, maybe they chose the one with the Laplacian, although it should also be specified if one considers smooth functions, distributions, or what - possibly this does not matter); I understand it relies on a choice of Riemannian metric (which in the Lie case is expected to be invariant), so I expect it addresses only the case of connected Lie groups (instead of general Lie groups, which include discrete groups).
Jul
27
comment On the global structure of the Gromov-Hausdorff metric space
Geodesic is a nice property (is there a reference) but this property of having a geodesic retraction to a point by self-similarities is much stronger and quite remarkable, so it would sound natural to ask if this only holds for the point corresponding to the singleton metric space, or for some others. Possibly stupid question: is GH homeomorphic/isometric to some Banach space?
Jul
27
comment When does equality occur in the triangle inequality in metric space?
On MathSE a more precise question would be required anyway, as well as some context.
Jul
27
comment Space of polynomially growing harmonic functions on a Lie group
"Harmonic function" on a group has no meaning; what makes sense is a harmonic function on a group endowed with a probability measure. And Kleiner's theorem is for the case of the uniform probability wrt a finite symmetric generating subset (probably it works on a more general setting, but maybe with some constraints anyway). In a locally compact (Lie or not) group, you need to be more specific about what you require about the probability measure (has density wrt Haar measure? compactly supported?), and also about the functions (continuous? measurable and $L^1$-loc?...).
Jul
27
comment On the global structure of the Gromov-Hausdorff metric space
Using the shrinking mentioned by Eric, we see that there is a distinguished point $o$ (the singleton metric space) such that there is a geodesic between any point in GH joining it to $o$ (the distance between any $X$ to $o$ equals the diameter of $X$), and since this shrinking is continuous, we see that $X$ is contractible. Natural questions are whether all other points in $X$ can be joined by geodesics, whether $X$ is locally path connected, locally contractible (in several possible senses), etc.