Nonsmooth Calabi-Yau algebras

Matt Booth (Lancaster University)

Tuesday 28th May 14:00-15:00 311B

Abstract

Calabi—Yau dg algebras, and their many-object cousins Calabi—Yau dg categories, are the analogues of Calabi—Yau manifolds in noncommutative derived geometry. A CY dg algebra is a smooth dg algebra such that the dualising complex is a shift of the diagonal bimodule. I'll talk about some recent work in progress, joint with Joe Chuang and Andrey Lazarev, about the sort of objects one gets when dropping smoothness from this definition. In particular, we show that nsCY dg algebras are Koszul dual to symmetric Frobenius coalgebras; we also show similar statements for Gorenstein vs. Frobenius and smooth vs. proper. As an application we derive a new characterisation of Poincaré duality spaces.

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