Tuesday, April 20, 14:00

Andreas Hochenegger (Milan), Formality of ℙ-objects.

Abstract:
An Calabi-Yau-object in a k-linear triangulated category is called a ℙ-object, if its derived endomorphism ring is isomorphic to k[t]/tⁿ.
They were first studied by Daniel Huybrechts and Richard Thomas as generalisations of spherical objects. Similar to the spherical case, ℙ-objects induce autoequivalences which are called ℙ-twists.
Ed Segal showed how an arbitrary autoequivalence can be written as a spherical functor. For a ℙ-twist, he needs the assumption that the endomorphism ring of the ℙ-object is formal.
In this talk, I will introduce the concept of formality and present a proof of the formality of configurations of ℙ-objects.
This is based on a joint work with Andreas Krug.