In this talk, I will present some techniques to deal with quaternionic slice regular functions in order to obtain global topological properties. These techniques come from abstract algebra and complex analysis. In particular, I will discuss the nature of quaternionic exponential and that of k-th roots as covering maps. I will try to present the topic with several explicit examples. The results are obtained in some works in collaboration with Chiara de Fabritiis and with Samuele Mongodi.