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Results tagged with geometric-group-theory
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user 33828
Large scale properties of groups; growth functions; Dehn functions; small cancellation properties; hyperbolicity and CAT(0); actions and representations; combinatorial group theory; presentations
1
vote
Actions of Thompson group F. II
The answer to the question as stated is yes, there is no binary tree as a subgraph for the standard action with standard generators (but there is a binary tree for some generating set). It follows fro …
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5
votes
Actions of Thompson group F
$F$ is bi-orderable, so if you care about actions by homeomorphisms on the line, you can pick up a bi-ordering and produce a dynamical realization: a faithful almost free action ( see Proposition 3.4 …
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6
votes
1
answer
500
views
Partition of a group into small subsets
A nonempty subset $S$ of a group $G$ is called small if there is an infinite sequence of elements $g_n$ in $G$ such that the translated sets $g_nS$ are pairwise disjoint.
Question: Is there a group …
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7
votes
1
answer
653
views
Growth of Thompson's group $F$
EDIT(August 2013): I accepted Mark's answer as being the state of art- there are two relevant references, one in the answer and one in the comments. The minimal growth rate of $F$ remains unknown with …
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5
votes
Trees in groups of exponential growth
This (so nice) question seems to be equivalent with the notorious and old problem of constructing a supraamenable (or superamenable) group of exponential growth. Recall that a supraamenable group is o …
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15
votes
3
answers
2k
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Folner sets and balls
Several related questions were asked before on MO, but it is not clear to me if the following was settled.
Given a finitely generated amenable group, is it always possible to find some finite genera …
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21
votes
3
answers
2k
views
The role of the Automatic Groups in the history of Geometric Group Theory
What is the role of the theory of Automatic Groups in the history of Geometric Group Theory?
Motivation:
When I read through the "Word Processing in Groups" I was amazed by the supreme beauty and el …
16
votes
0
answers
435
views
Splay trees and Thompson's group $F$
( I apologize for only indicating some easy to find references, but new users are not allowed to link more than five). This is very speculative, but:
Question: Is there a reformulation of the Dynamic …
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