Title: Topological analysis and experimental control of transformations of domain walls in magnetic cylindrical nanowires

Abstract: Topology is a powerful tool for categorizing magnetization textures, highlighting specific features in both 2D systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D nanomagnetism within confined geometries, the contributions from both volume and surface must be considered, requiring appropriate topological analysis to obtain a complete view of the system. Here, we consider domain walls in cylindrical magnetic nanowires to illustrate the use of topological invariants. We begin with micromagnetic simulations of domain wall transformation under the stimulus of an \OErsted field, tracking bulk and surface topological signatures, and analyzing the interplay between multiple micromagnetic objects. For instance, the extensive analysis allowed us to highlight mechanisms of domain wall type conversion from topologically non-trivial to trivial states, a phenomenon disregarded in previous studies. Additionally, we provide experimental evidence of the transient states predicted to occur during the dynamical process.