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Surface subgroups of graphs of free groups

Presented by: 
Henry Wilton
Wednesday 21st June 2017 - 11:30 to 12:30
INI Seminar Room 1
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons