Mathieu Carette

Chargé de recherches FNRS (Postdoctoral Researcher) Contact information: Université catholique de Louvain Département de Mathématiques Chemin du Cyclotron, 2 1348 Louvain-la-Neuve Belgique Email: firstname.lastname at uclouvain.be Office: b.025 Phone: +32(0)10 47 3158 Fax: +32(0)10 47 2530

• Groups acting on trees and their automorphisms
• Hyperbolic groups
• Coxeter groups

• On the rank of Coxeter groups. (with Richard Weidmann)
  Preprint (2009) pdf | arXiv | abstract

  Abstract:

  We show that the standard generating set of a Coxeter group is of minimal cardinality provided that the non-diagonal entries of the Coxeter matrix are sufficiently large.

• The automorphism group of accessible groups.
  Preprint (2008), To appear in J. London Math. Soc. pdf | arXiv | abstract

  Abstract:

  In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by taking extensions of relative automorphism groups of vertex groups, groups of Dehn twists and groups of automorphisms of free products. We apply this description and obtain a criterion for Out(G) to be finitely presented, as well as a necessary and sufficient condition for Out(G) to be finite. Consequences for hyperbolic groups are discussed.