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SUMMARY:Abigail Hollingsworth (University of Warwick)
DTSTART:20260611T123000Z
DTEND:20260611T133000Z
DTSTAMP:20260715T102336Z
UID:GaTO/143
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/143/">A
 ngle structures and representations through Dehn surgery space</a>\nby Abi
 gail Hollingsworth (University of Warwick) as part of Geometry and topolog
 y online\n\nLecture held in Room B3.02 in the Zeeman Building\, University
  of Warwick.\n\nAbstract\nLet $T$ be an ideal triangulation of a three-man
 ifold $M$. The shapes of the tetrahedra in the triangulation give gluing e
 quations\, the solutions to which we call the "shape variety". We look at 
 the real locus of the shape variety where the tetrahedra are all flat. The
 re are three types of angle structure that exist with flat tetrahedra.\n\n
 After Thurston sketched the boundary of Dehn surgery space of the figure-e
 ight knot\, Hodgson broke it down into three types\, which we denote as re
 presentations from the fundamental group of the knot complement into $\\ma
 thrm{PSL}(2\,\\mathbb{R})$\, $\\mathrm{PGL}(2\,\\mathbb{R})$\, and $\\math
 rm{SO}(3)$.\n\nWhat different angle structures have which types of represe
 ntation? Can they then also be deformed into a positive volume manifold su
 ch that all tetrahedra are positive? We will look at all the different com
 binations and determine which ones can exist.\n
LOCATION:https://researchseminars.org/talk/GaTO/143/
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