Local index theorem for projective families

TL;DR

This paper presents a superconnection proof of the cohomological index theorem for twisted Dirac operator families, extending previous results under less restrictive conditions.

Contribution

It provides a new proof technique for the index theorem using superconnections, relaxing earlier assumptions.

Findings

Superconnection proof simplifies the index theorem derivation.

Extends the theorem to broader classes of twisted Dirac operators.

Enhances understanding of index theory in twisted settings.

Abstract

We give a superconnection proof of the cohomological form of Mathai-Melrose-Singer index theorem for the family of twisted Dirac operators under relaxed conditions.