The cyclic Deligne conjecture and Calabi-Yau structures

组织者

深谷賢治 , 高鸿灏 , 袁航

演讲者

Chris Brav

时间

2024年11月20日 14:00 至 15:00

地点

Shuangqing-C546

线上

Zoom 388 528 9728 (BIMSA)

摘要

The Deligne conjecture, many times a theorem, states that for a dg category C, the dg endomorphisms End(Id_C) of the identity functor-- that is, the Hochschild cochains-- carries a natural structure of 2-algebra. When C is endowed with a Calabi-Yau structure, then Hochschild cochains and Hochschild chains are identified up to a shift, and we may transport the circle action from Hochschild chains onto Hochschild cochains. The cyclic Deligne conjecture states that the 2-algebra structure and the circle action together give a framed 2-algebra structure on Hochschild cochains. We establish the cyclic Deligne conjecture, as well as a variation that works for relative Calabi-Yau structures on dg functors D --> C, more generally for functors between stable infinity categories. We discuss examples coming from oriented manifolds with boundary, Fano varieties with anticanonical divisor, and doubled quivers with preprojective relation. This is
joint work with Nick Rozenblyum.