A Spectral Gap for Spinors on Hyperbolic Surfaces

Abstract

The purpose of this note is to construct a sequence of spin hyperbolic surfaces $\hat{I}{\pounds }_n$ with genus going to infinity and with a uniform spectral gap for the Dirac operator. Our construction is completely explicit. In particular, the $\hat{I}{\pounds }_n$ can be taken to be a tower of covers, with each $\hat{I}{\pounds }_n$ an arithmetic hyperbolic surface.

13 pages, comments welcome!