Smooth Calabi-Yau structures and the noncommutative Legendre transform

Maxim Kontsevich, Alex Takeda, Yiannis Vlassopoulos

We elucidate the relation between smooth Calabi-Yau structures and pre-Calabi-Yau structures. We show that, from a smooth Calabi-Yau structure on an $A_{\infty }$-category $A$, one ca…