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Surface subgroups of graphs of free groups

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NPCW05 - Group actions and cohomology in non-positive curvature

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.

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

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