course: Volumes, bounded cohomology and representations of three-manifold groups Part III
speaker: Marc Burger (ETH Zürich)abstract: In 1982 Gromov introduced bounded cohomology and showed that the bounded cohomology of a topological space is isometrically isomorphic to the bounded cohomology of its fundamental group. This result is at the basis of most rigidity results proven with cohomological methods. When dealing with manifolds with boundary, the use of bounded cohomology relative to the boundary components is paramount.
In this minicourse we present some of the results in relative bounded cohomology parallel to the one in relative cohomology and we show some applications to the study of the bounded cohomology of the fundamental group of appropriate graphs of groups.
Further, we define the volume of a representation of a three-manifold group and we prove some of its properties. As a corollary we obtain rigidity results for such representations into the isometry group of real hyperbolic space.
In a different direction, but for the same manifold groups, we define the volume of a representation into SL(n,C), prove that it satisfies a Milnor-Wood type inequality and study the properties of its maximality.
timetable:
Wed 18 Jun, 10:30 - 11:30, Aula Dini
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