BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Juan-Ramón Gómez-García (Institut de Mathématiques de Jussieu- Paris Rive Gauche) DTSTART:20260211T100000Z DTEND:20260211T110000Z DTSTAMP:20260423T021443Z UID:TQFT/162 DESCRIPTION:Title: D efect skein theory\, parabolic restriction and the Turaev coproduct\nb y Juan-Ramón Gómez-García (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as part of Topological Quantum Field Theory Club (IST\, Lisbo n)\n\n\nAbstract\nInspired by Jaeger’s composition formula for the HOMFL Y polynomial\, Turaev defined a coproduct on the HOMFLY skein algebra of a framed surface S\, turning it into a bialgebra. Jaeger’s formula can be viewed as a universal version of the restriction of the defining represen tation from GL_m+n to GL_m x GL_n. The restriction functor\, however\, is not braided\, and therefore there is a priori no reason for the induced li near map between the corresponding skein algebras to be multiplicative. In this talk\, I will address this problem using defect skein theory and the formalism of parabolic restriction.\n\nIn the first part of the talk\, I will introduce skein theory for 3-manifolds with both surface and line def ects. Local relations near the defects are produced from the algebraic dat a of a central algebra (codimension 1) and a centred bimodule (codimension 2). Examples of such structures are provided by the formalism of paraboli c restriction. In the second part of the talk\, I will explain how to cons truct a universal version of this formalism. Finally\, we will see how Tur aev’s coproduct extends to the entire skein category using the previous constructions.\n LOCATION:https://researchseminars.org/talk/TQFT/162/ END:VEVENT END:VCALENDAR