Noncommutative differential calculus, homotopy BV algebras and formality conjectures

TL;DR

This paper introduces strongly homotopy BV algebras, applies them to deformation theory, and formulates formality conjectures for Hochschild and cyclic chains, providing partial proofs.

Contribution

It defines strongly homotopy BV algebras and uses them to formulate and support formality conjectures in deformation theory.

Findings

Partial results support the formality conjectures.

New framework for homotopy BV algebras in deformation problems.

Connections between homotopy BV structures and Hochschild/cyclic chains.

Abstract

We define a notion of astrongly homotopy BV algebra and apply it to deformation theory problems. Formality conjectures for Hochschild and cyclic chains are formulated. We prove some partial results supporting these conjectures.