Large scale properties of groups; growth functions; Dehn functions; small cancellation properties; hyperbolicity and CAT(0); actions and representations; combinatorial group theory; presentations

learn more… | top users | synonyms

9
votes
1answer
304 views

Decidability of conjugacy problem for finitely generated subgroups of free groups

The conjugacy problem for a free group $F_n$ on $n$ letters has an easy solution. Each element of $F_n$ is conjugate to a unique and easily computable "cyclically reduced element" (this means that if ...
7
votes
2answers
281 views

Automorphisms of supergroups of non-coHopfian groups

In this question, I asked whether there existed groups $G$ with finitely presentable subgroups $H$ such that $gHg^{-1}$ is a proper subgroup of $H$ for some $g \in G$. Robin Chapman pointed out that ...
8
votes
1answer
437 views

Conjugating a subgroup of a group into a proper subgroup of itself

The following question came up in the class I'm teaching right now. There definitely exist groups $G$ with subgroups $H$ such that there exists some $g \in G$ such that $g H g^{-1}$ is a proper ...
11
votes
1answer
797 views

Topological HNN extensions

First, let me recall what an abstract HNN extension is. Let $G$ be an abstract group, $A, B < G$ be subgroups of $G$ and $\phi : A \to B$ be an isomorphisms. Then there is a group $H$ and an ...
1
vote
1answer
217 views

blowing up the graphs

I heard the phrase from many mathematician using in the colloquials. I heard algebraic geometer using it. I was never bother about it until one of my professor responded to one my question as follows: ...
5
votes
1answer
252 views

Connections between properties of a group and local symmetries of its Cayley graph

Hi everyone, Let $\Gamma$ be a finitly generated group. Does someone know of a connection between properties of $\Gamma$ to local symmetries of its Cayley graph? More specificly, what can one learn ...
4
votes
2answers
394 views

HNN extensions which are free products

which HNN-extensions are free products? this question is related with another still unsolved about Nielsen-Thruston-reducibility and connected-sum-irreducibility of 3d-torus- bundles...
3
votes
1answer
314 views

How do Dehn functions of special linear and mapping class groups behave?

Hi, I apologize for the basic questions. I am looking for good references on the following problems: 1) What is known about the Dehn function of $SL_n(\mathbb{Z})$? 2) What is known about the Dehn ...
23
votes
9answers
5k views

Introductory text on geometric group theory?

Can someone indicate me a good introductory text on geometric group theory?