Sergei Tabachnikov, Thesis Supervisor Nathanial Patrick Brown, Thesis Honors Advisor
Keywords:
topology sphere eversion mathematics
Abstract:
In this honors thesis, we investigate the topological problem of everting the 2-sphere in 3-space, i.e. turning a sphere inside out via continuous change allowing self-intersection but not allowing tearing, creasing, or pinching. The result was shown to exist by an abstract theorem proven in the 1950s, but the first explicit construction was not published until almost a decade later. Throughout the past 60 years, many constructions have been made, each providing their own insight into the theory behind the problem. In the following pages, we study the history surrounding the problem, the theory that made it possible, and a myriad of explicit examples giving a solid foundation in descriptive topology.
