Geometrization of piecewise homeomorphisms of the circle [ Back ]

Date:
26.09.19   
Times:
15:30
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Jérôme Los
University:
Institut de Mathématiques de Marseille

Abstract

In 1979 R. Bowen and C. Series gave a beautiful construction of a dynamical system associated to a Fuschian group. They constructed a particular map that was a piecewise diffeomorphism of the circle from the action of the group on the hyperbolic 2 space. More recently I generalized this idea to construct some piecewise homeomorphisms of the circle, for surface groups given by some particular group presentations.In this talk I’ll try to explain the reverse the question: How to construct a group from a piecewise homeomorphism on the circle and verify it is indeed a surface group? This is a geometrization problem and I will describe a construction for a class of such piecewise homeomorphisms of the circle.