Systole et rayon maximal des variétés hyperboliques non compactes

Matthieu Gendulphe (1)

1 Dipartimento di Matematica Guido Castelnuovo

We bound two global invariants of cusped hyperbolic manifolds: the length of the shortest closed geodesic (the systole), and the radius of the biggest embedded ball (the inradius). We give an upper bound for the systole, expressed in terms of the dimension and simplicial volume. We find a positive lower bound on the inradius independent of the dimension. These bounds are sharp in dimension 3, realized by the Gieseking manifold. It provides a new characterization of this manifold.

Mots clés: Hyperbolic manifolds; Cusps; Systole; Inradius

Domaines: Topologie géométrique [math.GT]

Matthieu Gendulphe. Systole et rayon maximal des variétés hyperboliques non compactes. 2011. ⟨hal-00612297⟩