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

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11
votes
1answer
795 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
215 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
250 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
390 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?