The IMAR Topology Seminar
Tuesday, November 24, 2020, 11:00
Title: Generalized Dehn twists on surfaces and surgeries in 3-manifolds
Abstract: (Joint work with Yusuke Kuno.) Given an oriented surface S and a simple closed curve C in S, the “Dehn twist” along C is the homeomorphism of S defined by “twisting” S around C by a full twist. If the curve C is not simple, this transformation of S does not make sense anymore, but one can consider two possible generalizations: one possibility is to use the homotopy intersection form of S to “simulate” the action of a Dehn twist on the (Malcev completion of) the fundamental group of S; another possibility is to view C as a curve on the top boundary of the cylinder S×[0,1], to push it arbitrarily into the interior so as to obtain, by surgery along the resulting knot, a new 3-manifold. In this talk, we will relate those two possible generalizations of a Dehn twist and we will give explicit formulas using a “symplectic expansion” of the fundamental group of S.
Speaker: Gwénaël Massuyeau (Université de Bourgogne)
For the skype zoom link please contact Radu Popescu (radu.popescu@imar.ro).
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