Jacob Caudell (Boston College)
Title:聽Lens space surgeries, lattices, and the Poincar茅聽homology sphere.
础产蝉迟谤补肠迟:听Moser's classification of Dehn surgeries on torus knots (1971) inspired a now fifty-years-old project to classify "exceptional" Dehn surgeries on knots in the three-sphere. A prominent component of this project seeks to classify which knots admit surgeries to the "simplest" non-trivial 3-manifolds--lens spaces. By combining data from Floer homology and the theory of integer lattices into the notion of a聽changemaker lattice, Greene (2010) solved the聽lens space realization problem:聽every lens space which may be realized as surgery on a knot in the three-sphere may be realized by a knot already known to surger to that lens space (i.e. a Berge knot). In this talk, we present a survey of techniques in Dehn surgery and their applications, introduce a lattice theoretic construction in the spirit of Greene's changemaker lattices, and discuss applications聽to surgeries on knots in the聽Poincar茅聽homology sphere.聽
For Zoom meeting please contact聽haedrich.alexandra [at] uqam.ca