Formalization of Bing’s shrinking method in geometric topology

Abstract

Bing’s shrinking method is a key technique for constructing homeomorphisms between topological manifolds in geometric topology. Applications of this method include the generalized Schoenflies theorem, the double suspension theorem for homology spheres, and the 4-dimensional Poincaré conjecture. Homeomorphisms obtained in this method are sometimes counter-intuitive and may even be pathological. This makes Bing’s shrinking method a good target of formalization by proof assistants. We report our formalization of this method in Coq/Ssreflect.