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May
2 |
comment |
What is the group of automorphisms of $l^{\infty}$?
The automorphism group of $l^\infty(X)$ will depend on what $X$ is. Also, what structure do you require automorphisms to preserve? |
Apr
25 |
revised |
Characteristically simple locally compact abelian groups
changed to exclude some trivial examples |
Apr
25 |
comment |
Characteristically simple locally compact abelian groups
Ah yes, I meant to exclude trivial examples like that (e.g. by also requiring $G$ to be locally elliptic). Indeed it is the TCS condition that gives some hope of a classification. It looks like all examples will have a compact open subgroup $U$ isomorphic to $\mathbb{Z}^{\mathbb{N}}_p$ with $G/U$ isomorphic to a direct sum of Prüfer $p$-groups, but there could be many ways of putting $U$ and $G/U$ together. |
Apr
23 |
asked | Characteristically simple locally compact abelian groups |
Feb
24 |
reviewed | Approve Berry-Esseen bound for martingale sequence with varying and dependent variances |
Feb
21 |
comment |
Dicks–Dunwoody almost stability theorem
Indeed, the translation is very straightforward in hindsight, but there have been a few papers spelling out the CAT(0) cube complex <-> median graph <-> space with walls <-> almost invariant set equivalences, so I didn't want to say it is completely obvious. Compactness of stabilisers is perhaps a strong enough assumption to get something better. |
Feb
21 |
revised |
Dicks–Dunwoody almost stability theorem
added 588 characters in body; edited title |
Feb
20 |
asked | Dicks–Dunwoody almost stability theorem |
Feb
17 |
awarded | Yearling |
Jan
7 |
comment |
When can a locally compact group be approximated by discrete subgroups?
I don't know if this helps for the application you have in mind, but for t.d.l.c. groups, an alternative way to approximate the group by discrete objects is to look instead at coset spaces $G/U$ where $U$ ranges over a base of identity neighbourhoods consisting of compact open subgroups. If $G$ is a SIN group, then you can also make $U$ normal in $G$, so $G/U$ is a discrete quotient group of $G$ in the natural sense. |
Jan
1 |
reviewed | Approve The injection of direct image sheaf |
Dec
10 |
reviewed | Approve Projective closure of affine curve |
Dec
10 |
reviewed | Approve Number of spanning trees which contain a given edge |
Dec
10 |
revised |
Distal actions on coset spaces
added 439 characters in body |
Dec
10 |
revised |
Can Calabi-Yau manifolds have nonabelian discrete symmetry groups?
edited tags |
Dec
7 |
revised |
Distal actions on coset spaces
added 175 characters in body |
Dec
7 |
asked | Distal actions on coset spaces |
Dec
6 |
reviewed | Approve Completion of modules of differentials (A strange exercise in Liu's AG textbook) |
Dec
5 |
reviewed | Approve Mystery behind ADE Dynkin diagram |
Dec
3 |
answered | Wild automorphisms of profinite groups |