Divergence terms in the supertrace heat asymptotics for the de Rham complex on a manifold with boundary

TL;DR

This paper employs invariance theory to compute a specific coefficient in the supertrace heat asymptotics for the twisted de Rham complex on manifolds with boundary, advancing understanding of boundary effects in geometric analysis.

Contribution

It introduces a method to determine the coefficient in the supertrace heat asymptotics for the twisted de Rham complex with boundary conditions.

Findings

Calculated the coefficient $a_{m+1,m}^{d+ heta}$ using invariance theory.

Extended heat asymptotics analysis to manifolds with boundary.

Provided explicit boundary term contributions in the supertrace expansion.

Abstract

We use invariance theory to determine the coefficient $a_{m+1,m}^{d+\delta}$ in the supertrace for the twisted de Rham complex with absolute boundary conditions.