Gilbert Levitt

A general construction of JSJ splittings.

Let G be a finitely generated group. Let A be any family of subgroups

of G, closed under taking subgroups and conjugates. Following

Forester, one says that two G-trees T, T' with edge groups in A are

in the same deformation space if they satisfy one of the following

equivalent conditions: T and T' are equivariantly quasi-isometric, T

and T' have the same elliptic subgroups, T and T' are related by a

finite sequence of elementary expansions and collapses. Deformation

spaces have a lot of structure, and one may extract many invariants.

If G is finitely presented, there always exists a JSJ deformation

space over A. Under additional hypotheses, it contains a preferred

splitting.

(This is joint work with Vincent Guirardel)