Subelliptic SpinC Dirac Operators, IV Proof of the Relative Index Conjecture

TL;DR

This paper proves the relative index conjecture for subelliptic SpinC Dirac operators, showing that embeddable deformations of certain CR-structures form a closed set in the smooth topology.

Contribution

It provides a proof of the relative index conjecture, linking index theory with the stability of CR-structure deformations.

Findings

Proves the relative index conjecture for subelliptic SpinC Dirac operators.

Shows the set of embeddable CR-structures is closed in the C-infinity topology.

Establishes a connection between index theory and CR-structure deformation stability.

Abstract

We prove the relative index conjecture, which in turn implies that the set of embeddable deformations of a strictly pseudoconvex CR-structure on a compact 3-manifold is closed in the C\infty-topology.