The Index Theorem for Toeplitz Operators as a Corollary of Bott Periodicity

TL;DR

This paper presents an expository analysis of the index of Toeplitz operators, demonstrating Boutet de Monvel's theorem as a consequence of Bott periodicity without relying on the Atiyah-Singer index theorem.

Contribution

It offers a novel proof of Boutet de Monvel's theorem derived from Bott periodicity, providing an alternative perspective independent of the Atiyah-Singer theorem.

Findings

Proof of Boutet de Monvel's theorem from Bott periodicity

Independent derivation of the index theorem for Toeplitz operators

Clarification of the relationship between Toeplitz index theory and Bott periodicity

Abstract

This is an expository paper about the index of Toeplitz operators, and in particular Boutet de Monvel's theorem. We prove Boutet de Monvel's theorem as a corollary of Bott periodicity, and independently of the Atiyah-Singer index theorem.