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Surface subgroups of graphs of free groups

Presented by: 
Henry Wilton University of Cambridge
Date: 
Wednesday 21st June 2017 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
A well known question, usually attributed to Gromov, asks whether every hyperbolic group is either virtually free or contains a surface subgroup. I’ll discuss the answer to this problem for the class of groups in the title when the edge groups are cyclic.  The main theorem is a result about free groups F which is of interest in its own right: whether of not an element w of F is primitive can be detected in the abelianizations of finite-index subgroup of F.  I’ll also mention an application to the profinite rigidity of the free group.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons