Global boundary conditions for a Dirac operator on the solid torus

TL;DR

This paper investigates a Dirac operator with Atiyah-Patodi-Singer boundary conditions on a solid torus, demonstrating the ellipticity of the boundary value problem and the existence of a compact parametrix.

Contribution

It establishes the ellipticity of the Dirac operator with specific boundary conditions on the solid torus, extending understanding of boundary value problems in geometric analysis.

Findings

The boundary value problem is elliptic.

The Dirac operator admits a compact parametrix.

Boundary conditions are compatible with ellipticity.

Abstract

We study a Dirac operator subject to Atiayh-Patodi-Singer like boundary conditions on the solid torus and show that the corresponding boundary value problem is elliptic, in the sense that the Dirac operator has a compact parametrix.