On the Hochschild cohomology of Tamarkin categories

TL;DR

This paper establishes a connection between the Hochschild cohomology of Tamarkin categories associated with open subsets of cotangent bundles and filtered symplectic cohomology, revealing a deep link between sheaf theory and symplectic topology.

Contribution

The paper proves that the Hochschild cohomology of Tamarkin categories is isomorphic to filtered symplectic cohomology, providing a new bridge between sheaf-theoretic and symplectic invariants.

Findings

Hochschild cohomology of Tamarkin categories matches filtered symplectic cohomology.

Establishes a new link between sheaf theory and symplectic topology.

Advances understanding of categorical invariants in symplectic geometry.

Abstract

To any open subset of a cotangent bundle, Tamarkin has associated a certain quotient of a category of sheaves. Here we show that the Hochschild cohomology of this category agrees with filtered symplectic cohomology.