Martin Lustig
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Martin Lustig has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- Yoav Moriah
Department of Mathematics, Technion, Haifa 32000, Israel
2 shared publications - François Gautero
Université Blaise Pascal (Clermont-Ferrand II), Campus des Cézeaux, Batiment de Mathématiques, Laboratoire de Mathématiques pures, 63177 Aubière, France
1 shared publication - Goulnara Arzhantseva
Section de Mathématiques, Université de Genève, CP 240, 1211 Genève 24, Switzerland
1 shared publication J.-Ph Pr Éaux
1 shared publication- Jean-Philippe Preaux
Laboratoire d'Analyse Topologie et Probabilités, UMR CNRS 7353, Aix-Marseille Université, 39 rue F.Joliot-Curie, 13453 Marseille Cedex 13, France
1 shared publication - Victor Guba
Vologda State University 15 Lenin Street 160600 Vologda Russia
1 shared publication
Latest Publications
- Open Access
Testing Cayley graph Densities (version longue)
We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: Given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m-generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2m. We test amenable and non-amenable groups, and also groups for which amenability is unknown. In the latter class we focus on Richard Thompson's group F. The sign means that we would like you to check our changes here. ♠
Open AccessTesting Cayley graph Densities (version longue)
We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: Given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m-generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2m. We test amenable and non-amenable groups, and also groups for which amenability is unknown. In the latter class we focus on Richard Thompson's group F. The sign means that we would like you to check our changes here. ♠
- 2 November 2004
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 137 (3) , 595-611
Relative hyperbolization of (one-ended hyperbolic)-by-cyclic groups
We show that the semi-direct product of a one-ended torsion-free word-hyperbolic group with $\integers$, given through an automorphism $\alpha{:}\, G \,{\to}\, G$, is a hyperbolic group relative to certain canonical subgroups of $G$ on which $\alpha$ acts periodically or with linear growth.- 2 November 2004
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 137 (3) , 595-611
Relative hyperbolization of (one-ended hyperbolic)-by-cyclic groups
We show that the semi-direct product of a one-ended torsion-free word-hyperbolic group with $\integers$, given through an automorphism $\alpha{:}\, G \,{\to}\, G$, is a hyperbolic group relative to certain canonical subgroups of $G$ on which $\alpha$ acts periodically or with linear growth.- Open Access
A finiteness result for Heegaard splittings
In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of $3g - 3$ disjoint essential disks. These are characterized by a combinatorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to fact that in general there can exist infinitely many such systems of disks which satisfy just the Casson-Gordon rectangle condition.Open AccessA finiteness result for Heegaard splittings
In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of $3g - 3$ disjoint essential disks. These are characterized by a combinatorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to fact that in general there can exist infinitely many such systems of disks which satisfy just the Casson-Gordon rectangle condition.