Indices of quaternionic complexes

TL;DR

This paper develops an algorithm to compute the analytical indices of elliptic complexes on quaternionic manifolds using characteristic classes, leading to topological obstructions for quaternionic structures.

Contribution

It introduces a novel algorithm for calculating indices of quaternionic complexes and derives topological obstructions for quaternionic structures on manifolds.

Findings

Algorithm for index computation using characteristic classes

Topological obstructions to quaternionic structures identified

Application to elliptic complexes on quaternionic manifolds

Abstract

Methods of parabolic geometries have been recently used to construct a class of elliptic complexes on quaternionic manifolds, the Salamon's complex being the simplest case. The purpose of this paper is to describe an algorithm how to compute their analytical indices in terms of characteristic classes. Using this, we are able to derive some topological obstructions to existence of quaternionic structures on manifolds.