  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.
