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Seminar Gæsteforelæsning

25.11.2024   at 15:00 - 16:00

QM Research Seminar: A universal characterization of uncurving

Speaker: Guillaume Laplante-Anfossi (University of Southern Denmark) 

Abstract:
Given a curved A-infinity algebra and a bounding cochain (a.k.a Maurer—Cartan element), one can twist the former by the latter to get a new A-infinity algebra where the curvature is zero. This uncurving procedure plays a central rôle in Floer theory, where Fukaya categories are naturally curved objects. The goal of this talk will be to give a universal characterization of the procedure, using the theory of operads: we will show that the operad cMC, whose algebras are curved A-infinity algebras endowed with a Maurer—Cartan element, together with its natural morphism to the A-infinity operad, is terminal in a certain comma category. This category does not contain the Maurer—Cartan equation, thus the theorem provides a way to « rediscover » it as the answer to a universal (algebraic) problem. This is joint work with Adrian Petr and Vivek Shende.