Topological surgery, dynamics and applications to natural processes

Abstract

In this paper, we observe that two-dimensional 0-surgery occurs in natural processes, such as tornado formation and other phenomena reminiscent of hole drilling. Inspired by such phenomena, we introduce new theoretical concepts which enhance the formal definition of two-dimensional 0-surgery with the observed dynamics. To do this, we first present a schematic model which extends the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on surfaces but are three-dimensional, we fill the interior space by defining the notion of solid two-dimensional 0-surgery. Finally, we connect these new theoretical concepts with a dynamical system and present it as a model for both two-dimensional 0-surgery and natural phenomena exhibiting it. We hope that through this study, topology and dynamics of many natural phenomena will be better understood.