Algebra, Topology and the Grothendieck-Teichmüller group

Towards a KRV2 action in the derived category

29 Aug 2022, 17:00

50m

Speaker

Chris Rogers (Reno)

Description

Let $X$ be a smooth complex variety. In previous joint work with V. Dolgushev and T. Willwacher, we exhibited an explicit action of ${\mathrm{GRT}}_1$ on the Gerstenhaber algebra $H^{\ast }(X,{\mathcal{T}}_{\mathrm{poly}})$. This action produces a large supply of nontrivial ${\mathrm{GRT}}_1$ representations. After reviewing this construction, I will discuss extending it to an action of ${\mathrm{KRV}}_2$ on the set of those isomorphisms $H^{\ast }(X,{\mathcal{T}}_{\mathrm{poly}})\cong H{H}^{\ast }(X)$ which correct the HKR map between the harmonic and Hochschild structures of $X$. A key ingredient is the recent characterization of ${\mathrm{KRV}}_2$ by Z. Dancso, I. Halacheva, and M. Robertson as automorphisms of a wheeled PROP. This is joint work in progress with M. Robertson.