The boundary of hyperbolic free-by-cyclic groups

Add to your list(s) Download to your calendar using vCal

• Yael Algom Kfir (University of Haifa)
• Wednesday 21 June 2017, 10:00-11:00
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact INI IT.

NPCW05 - Group actions and cohomology in non-positive curvature

Given an automorphism $\phi$ of the free group $F_n$ consider the HNN extension $G = F_n \rtimes_\phi \Z$. We compare two cases:
1. $\phi$ is induced by a pseudo-Anosov map on a  surface with boundary and of non-positive Euler characteristic. In this case $G$ is a CAT group with isolated flats and its (unique by Hruska) CAT -boundary is a Sierpinski Carpet (Ruane).
2. $\phi$ is atoroidal and fully irreducible. Then by a theorem of Brinkmann $G$ is hyperbolic. If $\phi$ is irreducible then Its boundary is homeomorphic to the Menger curve (M. Kapovich and Kleiner). 
We prove that if $\phi$ is atoroidal then its boundary contains a non-planar set. Our proof highlights the differences between the two cases above. 
This is joint work with A. Hilion and E. Stark.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.