Bounded cohomology and combinatorial volume forms

Duration: 52 mins 41 secs

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Description:	Frigerio, R Monday 19th June 2017 - 11:30 to 12:30


Created:	2017-07-17 15:14
Collection:	Non-Positive Curvature Group Actions and Cohomology
Publisher:	Isaac Newton Institute
Copyright:	Frigerio, R
Language:	eng (English)


Abstract:	Co-authors: Federico Franceschini (KIT Karlsruhe), MAria Beatrice Pozzetti (University of Warwick), Alessandro Sisto (ETH Zurich) In this talk we describe a family of 3-dimensional combinatorial volume forms on non-abelian free groups. These forms define non-trivial classes in bounded cohomology, and they may be exploited to show that, in degree 3, the zero norm subspace of the bounded cohomology of an acylindrically hyperbolic group is infinite dimensional. If time is left, as another application of combinatorial volume forms, we provide a purely cohomological proof of a lower bound, originally due to Brock, on the volume of the mapping torus of a cobounded pseudo-Anosov homeomorphism of a closed surface in terms of its Teichmuller translation distance.

Abstract:

Co-authors: Federico Franceschini (KIT Karlsruhe), MAria Beatrice Pozzetti (University of Warwick), Alessandro Sisto (ETH Zurich)

In this talk we describe a family of 3-dimensional combinatorial volume forms on non-abelian free groups. These forms define non-trivial classes in bounded cohomology, and they may be exploited to show that, in degree 3, the zero norm subspace of the bounded cohomology of an acylindrically hyperbolic group is infinite dimensional.

If time is left, as another application of combinatorial volume forms, we provide a purely cohomological proof of a lower bound, originally due to Brock, on the volume of the mapping torus of a cobounded pseudo-Anosov homeomorphism of a closed surface in terms of its Teichmuller translation distance.

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