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Infinite Volume and Bounded Cohomology

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James Farre
University of Utah
Mon, 15/04/2019 - 16:30 - 17:30
MPIM Lecture Hall

The bounded cohomology of a group encodes a wealth of geometric and algebraic data. We will define bounded cohomology of groups and construct explicit examples in dimension three; they come from
computing the volumes of locally geodesic tetrahedra in hyperbolic manifolds. It turns out that these volume classes distinguish the bi-Lipschitz classes of hyperbolic structures of infinite volume on a fixed 3-manifold, a fact that we will use to interpret addition in bounded cohomology as a kind of `geometric connected sum’ on hyperbolic manifolds.

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