Hyperbolicity of mapping-torus groups and spaces

François Gautero (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

This paper deals with the geometry of metric "two dimensional" spaces, equipped with semi-flows admitting transverse foliations by forests. Our main theorem relates the Gromov-hyperbolicity of such spaces, for instance mapping-telescopes of trees, with the dynamical behaviour of the semi-flow. As a corollary, we give a new proof of Bestvina-Feighn combination theorem for mapping-tori of injective free groups endomorphisms.

Mots clés: Gromov-hyperbolicity; mapping-tori; free groups endomorphisms; combination theorem; semi-flows

Domaines: Géométrie métrique [math.MG]

François Gautero. Hyperbolicity of mapping-torus groups and spaces. L'Enseignement Mathématique , 2003, 49 (2), pp.263-305. ⟨hal-00922273⟩