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A hyperbolic manifold fibering over the circle (and a theorem of Ian Agol and Dani Wise)

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Conférencier : Prof. Nicolas Bergeron, Sorbonne Université.
Date de l'événement : mardi 04 décembre 2018 16:30 - 18:30
Lieu : Belval campus
Maison du Savoir, room 3.520

This conference is part of the MAST Lecture Series organised by the Mathematics Department of the University of Luxembourg with the support of the FNR. The objective is to share the most recent developments of mathematics and their applications in the Luxembourg scientific community.

Abstract
In 1979 Jorgensen surprised geometers by constructing a 3-dimensional hyperbolic manifold fibering over the circle. Thirty-three years later Agol, using deep works of Wise, settled positively a question raised by William Thurston by proving that in fact every hyperbolic 3-manifold has a finite cover that fibers over the circle. In this talk, following an idea of Thurston, I will first construct an explicit example of a 3-dimensional hyperbolic manifolds fibering over the circle. The construction is elementary and can be made completely visual. The presentation will consist of a succession of short films, made with Jos Leys. In commenting on these films, I will try to explain how some of the ideas behind this construction relate to some of the basic ideas of the breakthrough of Agol and Wise.

Speaker

Nicolas Bergeron is Professor of Mathematics at Sorbonne Université. He previously held a CNRS position at École Normale Supérieure (Paris) and the Université Paris-Sud. He has made key contributions to the understanding of the topology and geometry of locally symmetric spaces, arithmetic groups, and their cohomology. He was awarded a CNRS bronze medal in 2007, and is member of Institut Universitaire de France.

Lien: MAST Lecture Series
Nicolas Bergeron