An Application of the Index Theorem for Manifolds with Fibered Boundaries

TL;DR

This paper applies the index theorem for manifolds with fibered boundaries to compute the Dirac operator's index on Taub-NUT space with a specific instanton connection, linking geometric analysis with gauge theory.

Contribution

It demonstrates how the index formula for fibered boundary manifolds can be used in the context of Taub-NUT space and instanton connections, extending previous applications.

Findings

Computed the Dirac operator index on Taub-NUT space with anti-self-dual instanton

Connected index theory with geometric analysis of specific gravitational instantons

Extended the application of index formulas to new geometric settings.

Abstract

We show how the index formula for manifolds with fibered boundaries can be used to compute the index of the Dirac operator on Taub-NUT space twisted by an anti-self-dual generic instanton connection.