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SUMMARY:Surface groups among cubulated group - Henry Wilton (University of
  Cambridge)
DTSTART:20250827T100000Z
DTEND:20250827T110000Z
UID:TALK235306@talks.cam.ac.uk
DESCRIPTION:Free groups and surface groups are often thought of as cousins
 . One way to make this precise is through their subgroup structure: they s
 hare the property that every subgroup of infinite index is free. In fact\,
  it turns out that this property characterises free and surface groups amo
 ng cubulated hyperbolic groups\, and also among other natural classes incl
 uding one-relator groups. I will discuss these results and their proofs. T
 he main new tool is the &ldquo\;Whitehead complex&rdquo\; associated to a 
 convex subcomplex of a CAT(0) cube complex. The Whitehead complex generali
 ses the classical Whitehead graph used to study automorphisms of free grou
 ps.
LOCATION:Seminar Room 2\, Newton Institute
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