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  • 0 posts edited
  • 3 helpful flags
  • 38 votes cast
Nov
24
awarded  Popular Question
Nov
16
revised Higher connectedness of Rips complexes
added 521 characters in body
Nov
16
comment Higher connectedness of Rips complexes
I was not clear enough, sorry: I redefine a group $G$ to be coarsely $n$-connected if for every $k\leq n$ and every finite subset $F\subset G$ there is a finite subset $F'\subset G$ with $F\subset F'$ such that $\pi_k$ applied to the inclusion $Rips_F(G)\rightarrow Rips_{F'}(G)$ is trivial.
Nov
16
comment Higher connectedness of Rips complexes
What do you mean? At least I did not choose any metric in advance. That's what I meant with "metric-independent". @HJRW: For some choice of metric if you want.
Nov
16
comment Higher connectedness of Rips complexes
Corrected the metric, thanks. Maybe there is also a way to state this metric-independent: For any finite subset $F\subset G$ we define $Rips_F(G)$ to be the complex with simplices $(x_1,...,x_n)$ such that there is $g\in G$ with $x_i\in gF$ for all $i$. Does this work? The point in the question is that I don't quite understand why the "strong connectivity" holds for dimensions $n=0,1$ but not for higher $n$.
Nov
16
revised Higher connectedness of Rips complexes
added 30 characters in body
Nov
16
asked Higher connectedness of Rips complexes
Nov
8
awarded  Yearling
Sep
20
revised Modern mathematical books on general relativity
added 296 characters in body
Sep
11
comment Modern mathematical books on general relativity
Straumann's book looks interesting. I will have a closer look at it. I accepted the other answer because it is also legit and has more up-votes.
Sep
9
accepted Modern mathematical books on general relativity
Sep
7
awarded  Nice Question
Sep
7
revised Modern mathematical books on general relativity
added links to books
Sep
7
comment Modern mathematical books on general relativity
Just an introduction/the basics on the physics side, but as modern as possible on the math side.
Sep
6
asked Modern mathematical books on general relativity
Jun
5
comment Convex subcomplexes of CAT(0) cubical complexes
In addition to Anton Petrunin's answer below, maybe also this paper is of interest: arxiv.org/abs/1211.1871
Jan
7
comment Group cohomology with compact support
Complementing Yemon Choi's comment: Maybe you mean Prop. 7.5 on p. 209 in Brown's book.
Nov
8
awarded  Yearling
Sep
4
accepted Semidirect products with braid groups and type $F_\infty$
Sep
4
answered Semidirect products with braid groups and type $F_\infty$