Categorification’ of the normalized Seiberg-Witten invariants associated with links of isolated normal surface singularities (Zsolt Szilágyi, Babes-Bolyai University, Cluj Napoca, Roumanie)

26.07.2018 11:00

Abstract:
We start with a negative definite plumbed 3-manifold M, which can be realized as link of an isolated normal surface singularity. We assume that M is a rational homology sphere. A theorem of András Némethi relates the Seiberg-Witten invariant of M with a counting function Q associated with the dual graph of the resolution of the singularity.

Based on this theorem Tamás László and András Némethi construct from Q the ‘multivariable periodic constant’ using Ehrhart theory and which can be interpreted as the normalized Seiberg-Witten invariant of M. Moreover, they also construct a polynomial (in 1- and 2-node case), which can be thought as ‘categorification’ of the normalized Seiberg-Witten invariant. In joint work with Tamás László we extend this construction to the general case and we give a division algorithm to compute this polynomial.

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Bâtiment: Battelle

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