Several topological methods have been used successfully in the study of the hypercomplex analysis; for example, in the theory of functions of several complex variables (Grauert et al., in: Encyclopaedia of mathematical science, vol. 74, Springer, 1991, Hirzebruch, in: Topological methods in algebraic geometry, Classics in Mathematics. Reprint of the 1978 Edition. Springer, Berlin, 1995, Krantz, in Function theory of several complex variables, 2nd edn. American Mathematical Society, Providence, 2001), in the Clifford analysis (Sabadini et al. in Adv. Appl. Clifford Algebras 24:1131–1143, 2014), and in the theory of slice regular functions (Colombo et al. in Math Nachr 285:949–958, 2012). Particularly, the fiber bundle is one of these topological subjects that had an intensive development in a number of papers (Bernstein and Philips in Sci Am 245(1):122–137, 1981, Bleecker, in: Guage Theory and Variational Principles. Dover Books on physics Dover Books on mathematics. Courier Corporation, North Chelmsford, 2005, Bredon in Topology and geometry, Springer, Berlin, 1913, Cohen in The topology of fiber bundles, Stanford University, Stanford, 1998, Hatcher in Algebraic-Topology, Cambridge University Press, Cambridge, 2002, Husemoller in fibre bundles, 3rd edn, Springer, Berlin, 1993, Steenrod in The topology of fibre bundles, Princeton University Press, Princeton, 1951, Walschap in Metric structures in differential geometry, Springer, New York, 2004, Weatherall in Synthese 193:2389–2425, 2016). The aim of this work is to show how the Splitting Lemma and the Representation Formula intrinsically determine a fiber bundle over the space of quaternionic slice regular functions and as a consequence, several properties of this function space are interpreted in terms of sections, pullbacks and isomorphism of fiber bundles.

几种拓扑方法已成功用于超复杂分析的研究；例如，在几个复变量的函数理论中（Grauert 等人，在：数学科学百科全书，第 74 卷，Springer，1991，Hirzebruch，在：代数几何中的拓扑方法，数学经典。重印1978 年版。Springer，柏林，1995，Krantz，在几个复变量的函数理论，第 2 版。美国数学学会，普罗维登斯，2001），在 Clifford 分析（Sabadini 等人在 Adv. Appl. Clifford Algebras 24:1131 –1143, 2014），以及切片正则函数理论（Colombo et al. in Math Nachr 285:949–958, 2012）。特别是，纤维丛是这些拓扑主题之一，在许多论文中得到了深入的发展（Bernstein 和 Philips 在 Sci Am 245(1) 中：122–137, 1981, Bleecker, in: Guage Theory and Variational Principles。Dover 物理书籍 Dover 数学书籍。Courier Corporation, North Chelmsford, 2005, Bredon in Topology and geometry, Springer, Berlin, 1913, Cohen in The topology of fiber bundles, Stanford University, Stanford, 1998, Hatcher in Algebraic-Topology, Cambridge University Press, Cambridge, 2002, Husemoller在纤维束中，第 3 版，Springer，柏林，1993，Steenrod 在纤维束的拓扑结构中，普林斯顿大学出版社，普林斯顿，1951，Walschap 在微分几何中的度量结构中，Springer，纽约，2004，Weatherall 在综合中 193:2389 –2425, 2016)。这项工作的目的是展示分裂引理和表示公式如何本质上确定四元数切片正则函数空间上的纤维丛，因此，