On L-infinity morphisms of cyclic chains

TL;DR

This paper clarifies the role of an L-infinity morphism constructed via the S^1-equivariant Poisson Sigma Model, establishing its equivalence to Tsygan's cyclic formality conjecture and connecting deformation quantization with cyclic chains.

Contribution

It provides a clear interpretation of the L-infinity morphism and proves its equivalence to Tsygan's cyclic formality, linking deformation quantization to cyclic chain formality.

Findings

The L-infinity morphism aligns with Tsygan's cyclic formality conjecture.

The formality statement is shown to be equivalent to cyclic chain formality.

The work bridges deformation quantization and cyclic chain theory.

Abstract

Recently the first two authors constructed an L-infinity morphism using the S^1-equivariant version of the Poisson Sigma Model (PSM). Its role in deformation quantization was not entirely clear. We give here a "good" interpretation and show that the resulting formality statement is equivalent to formality on cyclic chains as conjectured by Tsygan and proved recently by several authors.