String structures and trivialisations of a Pfaffian line bundle

TL;DR

This paper advances categorial index theory by calculating the Pfaffian line bundle of real Dirac operators and demonstrating how string structures induce trivialisations of this bundle.

Contribution

It provides a detailed calculation of the Pfaffian line bundle in a categorial setting and links string structures to its trivializations, a novel connection in the field.

Findings

Explicit calculation of the Pfaffian line bundle for a family of real Dirac operators

Demonstration of how string structures lead to trivialisations of the Pfaffian line bundle

Contribution to the understanding of categorial index theory and line bundle trivializations

Abstract

The present paper is a contribution to categorial index theory. Its main result is the calculation of the Pfaffian line bundle of a certain family of real Dirac operators as an object in the category of line bundles. Furthermore, it is shown how string structures give rise to trivialisations of that Pfaffian.