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SUMMARY:Cone types of geodesics and quasigeodesics in groups - Patrick Nai
 rne\, University of Oxford
DTSTART:20240301T160000Z
DTEND:20240301T170000Z
UID:TALK209299@talks.cam.ac.uk
CONTACT:Alexis Marchand
DESCRIPTION:We will discuss a new characterisation of Gromov hyperbolic gr
 oups: a group G is Gromov hyperbolic if and only if\, for all rational num
 bers K\, there are only finitely many "cone types" of (K\,C)-quasigeodesic
 s. This work is joint with Sam Hughes and Davide Spriano. \n\nRoughly\, th
 e cone type of a quasigeodesic gamma consists of all the ways you can poss
 ibly continue gamma so that it is still a quasigeodesic.\n\nCannon proved 
 in 1984 that the fundamental group of a compact hyperbolic manifold (or ra
 ther\, the Cayley graph of such a group) has only finitely many cone types
  of geodesics. Later\, in 2000\, Holt and Rees generalised this result to 
 encompass quasigeodesics: they proved that a Gromov hyperbolic group has o
 nly finitely many cone types of (K\,C)-quasigeodesics provided that K is r
 ational. Sam\, Davide and I prove a strong converse to this result of Holt
  and Rees.
LOCATION:MR13
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