Asymptotic equivariant index of Toeplitz operators and relative index of CR structures

TL;DR

This paper presents a new proof of the Atiyah-Weinstein conjecture by employing equivariant Toeplitz operator calculus to analyze the index of Fourier integral operators and CR structures.

Contribution

It introduces a novel approach using equivariant Toeplitz calculus to prove the Atiyah-Weinstein conjecture, providing new insights into the index theory of CR structures.

Findings

Proof of the Atiyah-Weinstein conjecture using Toeplitz calculus

New method for computing the index of Fourier integral operators

Enhanced understanding of the relative index of CR structures

Abstract

Using equivariant Toeplitz operator calculus, we give a new proof of the Atiyah-Weinstein conjecture on the index of Fourier integral operators and the relative index of CR structures.