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SUMMARY:Kane Townsend (University of Technology Sydney)
DTSTART:20221007T010000Z
DTEND:20221007T020000Z
DTSTAMP:20260423T021450Z
UID:SiN/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/45/">Hyp
 erbolic groups with $k$-geodetic Cayley graphs</a>\nby Kane Townsend (Univ
 ersity of Technology Sydney) as part of Symmetry in Newcastle\n\n\nAbstrac
 t\nA locally-finite simple connected graph is said to be $k$-geodetic for 
 some $k\\geq1$\, if there is at most $k$ distinct geodesics between any tw
 o vertices of the graph. We investigate the properties of hyperbolic group
 s with $k$-geodetic Cayley graphs. To begin\, we show that $k$-geodetic gr
 aphs cannot have a "ladder-like" geodesic structure with unbounded length.
  Using this bound\, we generalise a well-known result of Papasoglu that st
 ates hyperbolic groups with $1$-geodetic Cayley graphs are virtually-free.
  We then investigate which elements of the hyperbolic group with $k$-geode
 tic Cayley graph commute with a given infinite order element.\n
LOCATION:https://researchseminars.org/talk/SiN/45/
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