Atiyah classes with values in the truncated cotangent complex

TL;DR

This paper derives an explicit formula for the truncated Atiyah class of complexes of vector bundles and shows the first truncated Chern class depends solely on the determinant.

Contribution

It provides a new explicit formula for the truncated Atiyah class and clarifies the dependence of the first truncated Chern class on the determinant.

Findings

Explicit formula for the truncated Atiyah class

First truncated Chern class depends only on the determinant

Enhanced understanding of vector bundle complexes

Abstract

We prove an explicit formula for the truncated Atiyah class of a bounded complex of vector bundles. Furthermore, we show that the first truncated Chern class of such a complex only depends on its determinant.