Cork twisting Schoenflies problem

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.