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SUMMARY:Jacob Caudell (Boston College)
DTSTART:20220225T160000Z
DTEND:20220225T171500Z
DTSTAMP:20260423T005705Z
UID:CIRGET/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CIRGET/62/">
 Lens space surgeries\, lattices\, and the Poincaré homology sphere.</a>\n
 by Jacob Caudell (Boston College) as part of CRM - Séminaire du CIRGET / 
 Géométrie et Topologie\n\nAbstract: TBA\n\nMoser's classification of Deh
 n surgeries on torus knots (1971) inspired a now fifty-years-old project t
 o classify "exceptional" Dehn surgeries on knots in the three-sphere. A pr
 ominent component of this project seeks to classify which knots admit surg
 eries to the "simplest" non-trivial 3-manifolds--lens spaces. By combining
  data from Floer homology and the theory of integer lattices into the noti
 on of a changemaker lattice\, Greene (2010) solved the lens space realizat
 ion problem: every lens space which may be realized as surgery on a knot i
 n the three-sphere may be realized by a knot already known to surger to th
 at lens space (i.e. a Berge knot). In this talk\, we present a survey of t
 echniques in Dehn surgery and their applications\, introduce a lattice the
 oretic construction in the spirit of Greene's changemaker lattices\, and d
 iscuss applications to surgeries on knots in the Poincaré homology sphere
 .\n
LOCATION:https://researchseminars.org/talk/CIRGET/62/
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