String-Math Seminar: GPV invariants and Dehn surgery

Seminar | September 17 | 2-3 p.m. | 402 LeConte Hall

 Ciprian Manolescu, UCLA

 Department of Mathematics

Gukov, Putrov and Vafa postulated the existence of some 3-manifold invariants, obtained by counting BPS states in the \(3d\), \(N=2\) theory \(T[M_3]\). The GPV invariants take the form of power series converging in the unit disk, and whose radial limits at the roots of unity give the Witten-Reshetikhin-Turaev invariants. Furthermore, these power series have integer coefficients, and should admit a categorification. An explicit formula for the power series exists for negative definite plumbings. In this talk I will explain what should be the analogue of the GPV invariants for manifolds with torus boundary (such as knot complements), and propose a Dehn surgery formula for these invariants. The formula is conjectural, but it can be made explicit in the case of knots given by negative definite plumbings with an unframed vertex. This is joint work (in progress) with Sergei Gukov.