Cork twisting Schoenflies problem

TL;DR

This paper explores a novel approach to the Schoenflies conjecture and the Andrews-Curtis conjecture using cork twisting operations on contractible manifolds, demonstrated through the Cappell-Shaneson homotopy sphere example.

Contribution

It introduces a new method involving cork twisting to address longstanding topological conjectures, providing a fresh perspective and initial demonstration.

Findings

Cork twisting can be applied to the Cappell-Shaneson sphere

Potential new pathways for approaching the Schoenflies conjecture

Insights into the Andrews-Curtis conjecture via handle-slide operations

Abstract

The stable Andrews-Curtis conjecture in combinatorial group theory is the statement that every balanced presentation of the trivial group can be simplified to the trivial form by elementary moves corresponding to "handle-slides" together with "stabilization" moves. Schoenflies conjecture is the statement that the complement of any smooth embedding S^3 into S^4 are pair of smooth balls. Here we suggest an approach to these problems by certain cork twisting operation on contractible manifolds, and demonstrate it on the example of the first Cappell-Shaneson homotopy sphere.