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awarded  Popular Question 
Nov
16 
revised 
Higher connectedness of Rips complexes
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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 "metricindependent". @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 metricindependent: 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 upvotes. 
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 $F_\infty$ 