Slice regular functions and orthogonal complex structures over $\mathbb{R}^8$

TL;DR

This paper explores octonionic slice regular functions using differential topology, proving an Open Mapping Theorem and suggesting applications in studying almost-complex structures in eight dimensions.

Contribution

It establishes a comprehensive Open Mapping Theorem for octonionic slice regular functions and links these functions to the study of eight-dimensional almost-complex structures.

Findings

Proved a full version of the Open Mapping Theorem for octonionic slice regular functions.

Connected slice regular functions to the analysis of almost-complex structures in 8D.

Opened new avenues for using slice regular functions in differential topology.

Abstract

This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path for a possible use of slice regular functions in the study of almost-complex structures in eight dimensions.