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SUMMARY:Daniel Woodhouse (Oxford)
DTSTART:20200602T150000Z
DTEND:20200602T153000Z
DTSTAMP:20260423T003231Z
UID:GaTO/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/11/">Qu
 asi-isometric rigidity of graphs of free groups with cyclic edge groups</a
 >\nby Daniel Woodhouse (Oxford) as part of Geometry and topology online\n\
 n\nAbstract\nLet \\(F\\) be a finitely generated free group.\nLet \\(w_1\\
 ) and \\(w_2\\) be suitably random/generic elements in\n\\(F\\).  Consider
  the HNN extension \\( G = \\langle F\, t \\\,{\\mid}\\\, t w_1\nt^{-1} = 
 w_2 \\rangle\\).  It is already known that \\(G\\) will be\none-ended and 
 hyperbolic.  What we have shown is that \\(G\\) is\n<i>quasi-isometrically
  rigid</i>.  That is\, if a finitely\ngenerated group \\(H\\) is quasi-iso
 metric to \\(G\\)\, then \\(G\\)\nand \\(H\\) are virtually isomorphic.  T
 he main argument\ninvolves applying a new proof of Leighton's graph coveri
 ng\ntheorem.\n\nOur full result is for finite graphs of groups with virtua
 lly\nfree vertex groups and and two-ended edge groups.  However the\nstate
 ment here is more technical\; in particular\, not all such\ngroups are qua
 si-isometrically rigid.\n\nThis is joint work with Sam Shepherd.\n
LOCATION:https://researchseminars.org/talk/GaTO/11/
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