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

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. Acknowledgements. This work was partly supported by GNSAGA of INdAM, by the INdAM project “Hypercomplex function theory and applications” and by the PRIN 2017 project “Real and Complex Manifolds” of the Italian Ministry of Education (MIUR). The third author is also supported by Finanzi-amento Premiale FOE 2014 “Splines for accUrate NumeRics: adaptIve models for Simulation Environ-ments” of MIUR. The authors are grateful to the anonymous referee for the precious suggestions.