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Results tagged with geometric-group-theory
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user 15728
Large scale properties of groups; growth functions; Dehn functions; small cancellation properties; hyperbolicity and CAT(0); actions and representations; combinatorial group theory; presentations
4
votes
0
answers
208
views
Image of the mapping class group of surfaces into automorphism group?
Let $S_{g,p}^n$ be a compact oriented surface of genus $g$ with $p$ punctures and $n$ boundary components, and $\operatorname{Mod}(S)$ and $\operatorname{PMod}(S)$ be the mapping class group and the p …
- 347
2
votes
0
answers
137
views
Term and theories about "relation-free" elements in a group?
For a group $G$, there are two elements a, b which are "relation-free",
i.e., there is no nonempty, reduced word $W(X,Y)$ such that $W(a,b)=1$ in $G$.
Is there any terminologies or theories for that?
…
- 347
2
votes
1
answer
500
views
Do commutator functor and intersection commute?
For two subgroups $A, B$ in $G$,
$[A,A] \cap [B,B] = [A\cap B, A \cap B]$?
At least, if $G$ is free, is the left contained in the right?
- 347
2
votes
0
answers
137
views
Image of the pure braid group under the Artin presentation into the automorphism group of th...
As I know, it is unknown that the image of the mapping class group of the surface and its Johnson filtration under the higher Johnson homomorphisms.
There are a relationship between the mapping class …
- 347