Some H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {H}$$\end{document}-Banach Modules and Fiber Bundles

This work presents a coordinate sphere bundle defined from theory of slice regular functions whose bundle projection and some real Banach spaces induce coordinate sphere bundles in which the quaternionic Banach modules of the slice regular functions of Bloch, Besov and Dirichlet are the base spaces. Finally, this work shows that Möbius invariant property of these quaternionic Banach modules defines pullback bundles or automorphisms on sphere bundles.