# Quaternionic structures

## TL;DR

This paper explores modules over quaternion algebra bundles, discussing their properties and applications to geometric structures on manifolds, including obstructions to quaternionic structures.

## Contribution

It provides a detailed account of modules over quaternion algebra bundles, including Morita equivalence, characteristic classes, and K-theory, with applications to geometry.

## Key findings

- Obstructions for almost quaternionic structures on 8-dimensional Spinc manifolds identified
- Modules over quaternion algebra bundles characterized and classified
- Connections to quaternionic and algebraic geometry established

## Abstract

Any oriented 4-dimensional real vector bundle is naturally a line bundle over a bundle of quaternion algebras. In this paper we give an account of modules over bundles of quaternion algebras, discussing Morita equivalence, characteristic classes and K-theory. The results have been used to describe obstructions for the existence of almost quaternionic structures on 8-dimensional Spinc manifolds and may be of some interest, also, in quaternionic and algebraic geometry.