All Questions
Tagged with mg.metric-geometry geometric-group-theory
9 questions
10
votes
1
answer
1k
views
CAT(0) groups that does not act on CAT(0) cubical complex
CAT(0) groups are groups that act on a CAT(0) space properly and cocompactly. If a group acts on a CAT(0) cubical complex properly and cocompactly, then of course it is a CAT(0) Group. I am wondering ...
- 1,598
3
votes
1
answer
171
views
Criterion for visuality of hyperbolic spaces
I am trying to understand the following sentence on p. 156 of Buyalo-Schroeder, Elements of asymptotic geometry: "Every cobounded, hyperbolic, proper, geodesic space is certainly visual."
Let $X$ be ...
- 97
18
votes
1
answer
400
views
Finitely generated groups with Hölder-exotic space of ends?
The space of ends of a finitely generated group is always homeomorphic to 0, 1, 2 points, or a Cantor set, and in which of these 4 cases it falls is governed by Stallings' characterization (wikipedia ...
- 63.9k
9
votes
4
answers
982
views
isometric embeddings of Cayley graphs in "nice" spaces
This is from a physicist I know and as may be expected, I am threading my way between poorly defined and poorly translated.
What groups have Cayley graphs (w.r.t. a fixed finite generating set, and ...
- 1,625
8
votes
0
answers
185
views
Sharp isoperimetry in the discrete Heisenberg group
The exact shape of the set which has the best isoperimetry in the continuous Heisenberg is (from what I know) a difficult open problem. This brought to wonder what is known in the discrete case?
More ...
- 4,432
6
votes
2
answers
575
views
Which groups are doubling?
A metric space $(M,d)$ is doubling if there exists $n$ such that every ball of radius $r$ can be covered by $n$ balls of radius $r/2$, for all $r$. For which f.g. groups $G$ and finite symmetric ...
- 6,652
6
votes
2
answers
729
views
Rationality of translation lengths in hyperbolic groups
Recall that the translation length $\tau(g)$ of an element $g \in G$ is the limit $d(1, g^n)/n$, where $d$ is the word metric on $G$ with resepct to some generating set.
It is a theorem of Gromov ...
- 619
5
votes
1
answer
242
views
Cancellation of elements in the Gromov boundary of a free group
Let $A$ be a finite set of free generators and their inverses and $F$ the free group generated by elements in $A$ (some call $A$ the alphabet of $F$). For each $g\in F$, use $\vert\,g\,\vert$ to ...
- 307
4
votes
3
answers
376
views
Proof that lifts of geodesics are quasi-geodesics (relatively hyperbolic groups)
$\DeclareMathOperator\Cay{Cay}$Suppose $G$ is a relatively hyperbolic group with peripheral subgroups $P_1,P_2,\dots, P_n$, and suppose $\mathcal{S}$ is a finite generating set for $G$. Let $X=\Cay(G,\...
- 421