Martin Lustig
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Martin Lustig has a total of 24 co-authors. Here are the top co-authors by number of shared publications:
- Ilya Kapovich
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA
9 shared publications - Yoav Moriah
Department of Mathematics, Technion, Haifa 32000, Israel
6 shared publications - Arnaud Hilion
LATP UMR 6632 Université Paul Cézanne, avenue escadrille Normandie Niemen 13397 Marseille cedex 20 France
4 shared publications - Thierry Coulbois
LATP, Université Aix-Marseille III, Marseille, France
4 shared publications Alan F. Beardon
1 shared publicationAndrew J. Duncan
1 shared publication
Latest Publications
- 15 September 2015
- Published by Mathematical Sciences Publishers in Pacific Journal of Mathematics
- Vol. 277 (2) , 371-398
Patterson–Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for outer space
Some minor updates and revisions; 18 pages, no figures.International audienceWe quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number
- 15 September 2015
- Published by Mathematical Sciences Publishers in Pacific Journal of Mathematics
- Vol. 277 (2) , 371-398
Patterson–Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for outer space
Some minor updates and revisions; 18 pages, no figures.International audienceWe quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number
- 1 January 2012
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2012 (670)
Are large distance Heegaard splittings generic?
27 pages 5 figuresInternational audienceIn a previous paper we introduced a notion of "genericity" for countable sets of curves in the curve complex of a surface S, based on the Lebesgue measure on the space of projective measured laminations in S. With this definition we prove that for each fixed g > 1 the set of irreducible genus g Heegaard splittings of high distance is generic, in the set of all irreducible Heegaard splittings. Our definition of "genericity" is different and more intrinsic then the one given via random walks
- 1 January 2012
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2012 (670)
Are large distance Heegaard splittings generic?
27 pages 5 figuresInternational audienceIn a previous paper we introduced a notion of "genericity" for countable sets of curves in the curve complex of a surface S, based on the Lebesgue measure on the space of projective measured laminations in S. With this definition we prove that for each fixed g > 1 the set of irreducible genus g Heegaard splittings of high distance is generic, in the set of all irreducible Heegaard splittings. Our definition of "genericity" is different and more intrinsic then the one given via random walks
- Open Access
Domains of proper discontinuity on the boundary of Outer space
Motivated by the work of McCarthy and Papadopoulos for subgroups of mapping class groups, we construct domains of proper discontinuity in the compactified Outer space and in the projectivized space of geodesic currents for any "sufficiently large" subgroup of $Out(F_N)$ (that is, a subgroup containing a hyperbolic iwip). As a corollary we prove that for $N\ge 3$ the action of $Out(F_N)$ on the subset of $\mathbb PCurr(F_N)$ consisting of all projectivized currents with full support is properly discontinuous.Open AccessDomains of proper discontinuity on the boundary of Outer space
Motivated by the work of McCarthy and Papadopoulos for subgroups of mapping class groups, we construct domains of proper discontinuity in the compactified Outer space and in the projectivized space of geodesic currents for any "sufficiently large" subgroup of $Out(F_N)$ (that is, a subgroup containing a hyperbolic iwip). As a corollary we prove that for $N\ge 3$ the action of $Out(F_N)$ on the subset of $\mathbb PCurr(F_N)$ consisting of all projectivized currents with full support is properly discontinuous. - Open AccessStabilizers of $\mathbb R$-trees with free isometric actions of $F_N$We prove that if $T$ is an $\mathbb R$-tree with a minimal free isometric action of $F_N$, then the $Out(F_N)$-stabilizer of the projective class $[T]$ is virtually cyclic. For the special case where $T=T_+(\phi)$ is the forward limit tree of an atoroidal iwip element $\phi\in Out(F_N)$ this is a consequence of the results of Bestvina, Feighn and Handel, via very different methods. We also derive a new proof of the Tits alternative for subgroups of $Out(F_N)$ containing an iwip (not necessarily atoroidal): we prove that every such subgroup $G\le Out(F_N)$ is either virtually cyclic or contains a free subgroup of rank two. The general case of the Tits alternative for subgroups of $Out(F_N)$ is due to Bestvina, Feighn and Handel.Open AccessStabilizers of $\mathbb R$-trees with free isometric actions of $F_N$We prove that if $T$ is an $\mathbb R$-tree with a minimal free isometric action of $F_N$, then the $Out(F_N)$-stabilizer of the projective class $[T]$ is virtually cyclic. For the special case where $T=T_+(\phi)$ is the forward limit tree of an atoroidal iwip element $\phi\in Out(F_N)$ this is a consequence of the results of Bestvina, Feighn and Handel, via very different methods. We also derive a new proof of the Tits alternative for subgroups of $Out(F_N)$ containing an iwip (not necessarily atoroidal): we prove that every such subgroup $G\le Out(F_N)$ is either virtually cyclic or contains a free subgroup of rank two. The general case of the Tits alternative for subgroups of $Out(F_N)$ is due to Bestvina, Feighn and Handel.
- 3 March 2011
- Published by Walter de Gruyter GmbH in Journal of Group Theory
Stabilizers of ℝ-trees with free isometric actions ofFN
- 3 March 2011
- Published by Walter de Gruyter GmbH in Journal of Group Theory
Stabilizers of ℝ-trees with free isometric actions ofFN
- 1 January 2011
- Published by Walter de Gruyter GmbH in Journal of Group Theory
- Vol. 14 (5) , 673-694
Stabilizers of ℝ-trees with free isometric actions of FN
We prove that if T is an ℝ-tree with a minimal free isometric action of FN, then the Out(FN)-stabilizer of the projective class [T] is virtually cyclic.
- 1 January 2011
- Published by Walter de Gruyter GmbH in Journal of Group Theory
- Vol. 14 (5) , 673-694
Stabilizers of ℝ-trees with free isometric actions of FN
We prove that if T is an ℝ-tree with a minimal free isometric action of FN, then the Out(FN)-stabilizer of the projective class [T] is virtually cyclic.
- Open Access
Are large distance Heegaard splittings generic ?
In a previous paper we introduced a notion of "genericity" for countable sets of curves in the curve complex of a surface S, based on the Lebesgue measure on the space of projective measured laminations in S. With this definition we prove that for each fixed g > 1 the set of irreducible genus g Heegaard splittings of high distance is generic, in the set of all irreducible Heegaard splittings. Our definition of "genericity" is different and more intrinsic then the one given via random walks.
Open AccessAre large distance Heegaard splittings generic ?
In a previous paper we introduced a notion of "genericity" for countable sets of curves in the curve complex of a surface S, based on the Lebesgue measure on the space of projective measured laminations in S. With this definition we prove that for each fixed g > 1 the set of irreducible genus g Heegaard splittings of high distance is generic, in the set of all irreducible Heegaard splittings. Our definition of "genericity" is different and more intrinsic then the one given via random walks.
- Open Access
Ping-pong and Outer space
We prove that if $\phi,\psi\in Out(F_N)$ are hyperbolic iwips (irreducible with irreducible powers) such that $<\phi,\psi>\le Out(F_N)$ is not virtually cyclic then some high powers of $\phi$ and $\psi$ generate a free subgroup of rank two, all of whose nontrivial elements are again hyperbolic iwips. Being a hyperbolic iwip element of $Out(F_N)$ is strongly analogous to being a pseudo-Anosov element of a mapping class group, so the above result provides analogs of "purely pseudo-Anosov" free subgroups of $Out(F_N)$.Open AccessPing-pong and Outer space
We prove that if $\phi,\psi\in Out(F_N)$ are hyperbolic iwips (irreducible with irreducible powers) such that $<\phi,\psi>\le Out(F_N)$ is not virtually cyclic then some high powers of $\phi$ and $\psi$ generate a free subgroup of rank two, all of whose nontrivial elements are again hyperbolic iwips. Being a hyperbolic iwip element of $Out(F_N)$ is strongly analogous to being a pseudo-Anosov element of a mapping class group, so the above result provides analogs of "purely pseudo-Anosov" free subgroups of $Out(F_N)$. - 1 January 2010
- Published by Springer Nature
- p. 243-250
The F N -action on the Product of the Two Limit Trees for an Iwip Automorphism
- 1 January 2010
- Published by Springer Nature
- p. 243-250
The F N -action on the Product of the Two Limit Trees for an Iwip Automorphism
- 1 September 2009
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 147 (2) , 345-368
ℝ-trees, dual laminations and compact systems of partial isometries
LetFNbe a free group of finite rankN≥ 2, and letTbe an ℝ-tree with a very small, minimal action ofFNwith dense orbits. For any basis ofFNthere exists aheart $K_{\CAr}$ ⊂ (= the metric completion ofT) which is a compact subtree that has the property that the dynamical system of partial isometriesai: $K_{\CAr} \cap a_{i} K_{\CAr} \to a_{i}\inv K_{\CAr} \cap K_{\CAr}$ , for eachai∈ , defines a tree $T_{(K_{\CAn}, \CAr)}$ which contains an isometric copy ofTas minimal subtree.- 1 September 2009
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 147 (2) , 345-368
ℝ-trees, dual laminations and compact systems of partial isometries
LetFNbe a free group of finite rankN≥ 2, and letTbe an ℝ-tree with a very small, minimal action ofFNwith dense orbits. For any basis ofFNthere exists aheart $K_{\CAr}$ ⊂ (= the metric completion ofT) which is a compact subtree that has the property that the dynamical system of partial isometriesai: $K_{\CAr} \cap a_{i} K_{\CAr} \to a_{i}\inv K_{\CAr} \cap K_{\CAr}$ , for eachai∈ , defines a tree $T_{(K_{\CAn}, \CAr)}$ which contains an isometric copy ofTas minimal subtree.