Stable cohomology of polyvector fields

TL;DR

This paper investigates the stable cohomology of algebraic polyvector fields on Euclidean space, revealing its structure as a symmetric product of the cohomology of Kontsevich's graph complex, with some known classes excluded.

Contribution

It establishes a precise description of the stable cohomology of polyvector fields in terms of Kontsevich's graph complex cohomology, advancing understanding in algebraic geometry and homological algebra.

Findings

Stable cohomology is the symmetric product of graph complex cohomology.

Identifies the structure of cohomology up to known classes.

Provides a link between polyvector fields and graph complexes.

Abstract

We show that the stable cohomology of the algebraic polyvector fields on $\mathbb{R}^n$, with values in the adjoint representation is the symmetric product space on the cohomology of M. Kontsevich's graph complex, up to some known classes.