Eta invariants with spectral boundary conditions

TL;DR

This paper investigates the asymptotic behavior of heat traces for Dirac-type operators with spectral boundary conditions, deriving boundary contributions to the expansion coefficients using functorial methods.

Contribution

It provides a detailed analysis of heat trace asymptotics with spectral boundary conditions, including explicit calculations of boundary terms.

Findings

Boundary part of leading coefficients determined

Functorial techniques applied to spectral boundary problems

Explicit calculations for special cases included

Abstract

We study the asymptotics of the heat trace $\Tr\{fPe^{-tP^2}\}$ where $P$ is an operator of Dirac type, where $f$ is an auxiliary smooth smearing function which is used to localize the problem, and where we impose spectral boundary conditions. Using functorial techniques and special case calculations, the boundary part of the leading coefficients in the asymptotic expansion is found.