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Gilbert Levitt

Many papers were written, circulated, but never published. The aim of this page is to collect them and make them available. Feel free to suggest additions!

Whenever possible I indicate the date, as well as published papers where the main results are proved.

Warning: These papers are interesting, but haven't been properly refereed, so beware...

A tout seigneur tout honneur, we start with the conjugacy problem in Out(F_n). Martin Lustig's 1994 announcement, which was distributed during a conference in Luminy, and the Max Planck preprints 1 2 (ps files).

Again by Martin, a 2004 paper with Jerome Los. They show contractibility of the set of efficient representatives of an irreducible automorphism of F_n, and they introduce a canonical folding in outer space (different from Skora's).

And a 2007 paper with François Gautero. They show that the mapping torus of an automorphism of F_n is hyperbolic relative to mapping tori of polynomial subgroups (these subgroups are defined in my 2009 paper on growth).

Anything else, Martin?

I mentioned Skora, I know two unpublished papers by him, both from 1989.

The first one studies free products with amalgamation and HNN extensions of actions on R-trees.

The second one is better known: he shows contractibility of outer space by defining a folding process. See Matt Clay's paper, and my paper with Vincent Guirardel.

The outer limits paper (1992, revised 1994). See my 1995 paper with Damien Gaboriau about the rank of actions for the dimension of compactified outer space, and Camille Horbez's recent paper for the fact that all very small trees belong to the boundary of outer space. I don't know a reference for Bestvina-Feighn's free group decomposition lemma (Lemma 4.1).

Arnaud wrote his thesis in 2004 on the action of a given automorphism of F_n on the union of F_n and its boundary. Most results are only available there (in French).

His second Nielsen-Thurston paper (1995). He constructs a hierarchical decomposition for automorphisms of F_n by studying periodic free factors.

Even Vincent has an unpublished paper (2001). Bestvina-Feighn gave a bound for the complexity of simplicial trees with small edge stabilizers. Vincent gives a bound for

Her paper about the boundary of the curve complex (1999).

In his thesis (1999) Shor proved that a torsion free hyperbolic group contains, up to isomorphism, only finitely many fixed subgroups of automorphisms. Paper

There is a proof in a paper I wrote with Martin Lustig (see also arXiv:1408.0418).

His 1995 thesis (ps file) constructs thin (exotic) measured foliations which are not uniquely ergodic, and discusses currents in free groups.

His 2001 thesis Algorithmic Properties of Relatively Hyperbolic Groups, showing that certain groups are biautomatic.

Gilbert Levitt

My contribution: I proved in arXiv:0810.0935 that the isomorphism problem is unsolvable for [free abelian]-by-free groups. But Bruno Zimmermann had published a similar result in 1985 (reference 13 in publications). His paper was in German, though. Reference 8 is another paper which is not sufficiently known: he showed (in 1981) that any finite subgroup of Out(F_n) may be realized as symmetries of a graph.

There seems to be a lost 1991 paper showing that "any finite subgroup fixes a point in McCullough-Miller space". Does anyone have it?

Gilbert Levitt Laboratoire LMNO, UMR 6139 (Equipe Algèbre, Géométrie, Logique) Université de Caen F14032 Caen Cedex Campus 2, S3 241 Tél. : +33 2 31 56 74 57 Fax : +33 2 31 56 73 20 levitt (at) unicaen.fr |