QGM seminar by Filippo Cerocchi (MPIM, Bonn)

Title: Compactness and convergence of non-geometric 3-manifolds of non-positive curvature

2017.10.12 | Jane Jamshidi

Date Wed 29 Nov
Time 16:30 17:30
Location 1531-215 (Aud. D3)

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.