# Compactness and convergence of non-geometric 3-manifolds of non-positive curvature

Filippo Cerocchi
(MPIM, Bonn)
Seminar
Wednesday, 29 November, 2017, at 16:30-17:30, in Aud. D3 (1531-215)
Abstract:
We shall give a proof of the precompactness (with respect to the Gromov-Hausdorff topology) of the set of non-positively curved, closed, non-geometric 3-manifolds with bounded entropy and diameter. This will be achieved by using as main tools the barycenter method of Besson-Courtois-Gallot and two results that we proved with Andrea Sambusetti: namely a systolic estimate for non-geometric 3-manifolds with bounded entropy and diameter and an inequality -- holding for finitely generated groups which possess acylindrical splittings -- relating the entropy of a finitely generated group G with respect to a given (finite) generating set S to the cardinality of S. Moreover, we shall describe the features of the metric spaces arising as Gromov-Hausdorff limits of the manifolds in this set. This is a joint work with Andrea Sambusetti.
Organised by: QGM
Contact person: Cristiano Spotti, Martin de Borbon & Roberta Iseppi