Immersed and virtually embedded -injective surfaces in graph manifolds.
Injective morphisms between Artin-Tits groups. (Morphismes injectifs entre groupes d'Artin-Tits.)
Isometries of systolic spaces
We provide a classification of isometries of systolic complexes corresponding to the classification of isometries of CAT(0)-spaces. We prove that any isometry of a systolic complex either fixes the barycentre of some simplex (elliptic case) or stabilizes a thick geodesic (hyperbolic case). This leads to an alternative proof of the fact that finitely generated abelian subgroups of systolic groups are undistorted.
conjecture for Artin groups
The purpose of this paper is to put together a large amount of results on the conjecture for Artin groups, and to make them accessible to non-experts. Firstly, this is a survey, containing basic definitions, the main results, examples and an historical overview of the subject. But, it is also a reference text on the topic that contains proofs of a large part of the results on this question. Some proofs as well as few results are new. Furthermore, the text, being addressed to non-experts, is as...
groups are almost convex and have a sub-cubic Dehn function.
L²-homology and reciprocity for right-angled Coxeter groups
Let W be a Coxeter group and let μ be an inner product on the group algebra ℝW. We say that μ is admissible if it satisfies the axioms for a Hilbert algebra structure. Any such inner product gives rise to a von Neumann algebra containing ℝW. Using these algebras and the corresponding von Neumann dimensions we define -Betti numbers and an -Euler charactersitic for W. We show that if the Davis complex for W is a generalized homology manifold, then these Betti numbers satisfy a version of Poincaré...
L2-Topological invariants of 3-manifolds.
Limit groups and groups acting freely on -trees.
Limit groups for relatively hyperbolic groups. II: Makanin-Razborov diagrams.
Limits of (certain) CAT(0) groups. I: Compactification.
Linear representations of the group of conjugating automorphisms and the braid groups of some manifolds.
L'ordre de Dehornoy sur les tresses
Mapping tori of free group automorphisms are coherent.
Milnor-Wood inequality for crystallographic groups
Morita classes in the homology of automorphism groups of free groups.
Nonpositive immersions, sectional curvature, and subgroup properties.
Non-positively curved aspects of Artin groups of finite type.
On chirality groups and regular coverings of regular oriented hypermaps
We prove that if the Walsh bipartite map of a regular oriented hypermap is also orientably regular then both and have the same chirality group, the covering core of (the smallest regular map covering ) is the Walsh bipartite map of the covering core of and the closure cover of (the greatest regular map covered by ) is the Walsh bipartite map of the closure cover of . We apply these results to the family of toroidal chiral hypermaps induced by the family of toroidal bipartite maps...
On finite subgroups of groups of type VF.
On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number.