Geometric Group Theory in Bonn II

GGT in Bonn












An application of TQFT to a question of Ivanov
Gregor Masbaum (IMJ-PRG/MPIM)

Abstract: We use TQFT to compute the intersection of all maximal finite index subgroups of the mapping class group of an orientable surface. This partially answers a question of Ivanov, who was motivated by the famous open question whether mapping class groups are linear. (Joint work with A. Reid.)

Sphere boundaries of hyperbolic groups
Nir Lazarovich (ETH)

Abstract: We show that the boundary of a one-ended simply connected at infinity hyperbolic group with enough codimension-1 surface subgroups is homeomorphic to a sphere. By works of Markovic and Kahn-Markovic our result gives a new characterization of groups which are virtually fundamental groups of hyperbolic 3-manifolds. Joint work with B. Beeker.

Curve and arc graphs for infinite type surfaces
Hugo Parlier (Fribourg)

Abstract: Curve, arc and pants graphs have been useful tools for studying the large scale geometry of Teichm├╝ller spaces and mapping class groups for finite surfaces. This talk will be about ways to define and study analogous objects for infinite type surfaces. Based on joint work with J. Aramayona and A. Fossas.

Ultralimits of maximal representations
Beatrice Pozzetti (Warwick)

Abstract: A representation of the fundamental group of an hyperbolic surface in the symplectic group Sp(2n,R) is called maximal if it maximize the socalled Toledo invariant. Maximal representations form interesting and well studied components of the character variety generalizing the Teichmuller component, that correspond to the case n=1. Given an unbounded sequence of maximal representations one naturally gets an action on an affine building. I will describe geometric properties of such actions, dealing in particular with the structure of elements acting with a fixed point. Joint work with Marc Burger.

Systems of curves and systoles on surfaces
Federica Fanoni (Warwick)

Abstract: I will talk about two types of sets of curves on surfaces, k-systems and k-filling sets. These are defined by purely topological constraints, such as bounds on the number of intersections. I will discuss two problems in this setting: bounding the size of these sets and understanding what happens to these bounds when the surface is endowed with a hyperbolic structure and the curves are required to be systoles (shortest closed geodesics). This is joint work with Hugo Parlier.