Differential forms on the moduli stack of perfect complexes (II)

Perfect complexes are finite rank graded vector spaces with a differential of degree +1, and more generally, twisted complexes of vector bundles over a manifold. There is a generalization of the theory of characteristic classes to this setting - a major complication, however, is that the holonomy of a connection is no longer necessarily invertible, but only quasi-invertible.

In this second talk, we will give an explicit formula for the Chern character of a perfect complex. Our formulas are explicit, unlike in the original construction of Toën and Vezzosi, who used the cobordism hypothesis to prove existence.