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arXiv · 1807.05899

Holomorphicity of slice-regular functions

Samuele Mongodi
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Abstract

Slice-regular functions of a quaternionic variable have been studied extensively in the last 12 years, resulting, in many ways, quite close to classical holomorphic functions of a complex variable; indeed, there is a correspondence between slice-regular functions and a certain family of holomorphic maps from the complex plane to $\mathbb{C}^4$, as noted by Ghiloni and Perotti. However, such a construction does not seem to offer any insight on the behaviour of slice-regular functions, due to the lack of a connection between the values of the holomorphic map and the values of the associated sliceregular function. The aim of this work is to show that there is indeed a (complex) geometric way to relate the values of this two functions, thus relating more deeply the world of holomorphic functions with that of slice-regular functions.

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Samuele Mongodi. 2018-07-16. Holomorphicity of slice-regular functions. https://arxiv.org/abs/1807.05899

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