An exotic presentation of ℤ × ℤ and the Andrews–Curtis conjecture

Abstract

We prove that the presentations hx; y j Œx; y ; 1i and hx; y j Œx; Œx; y 1 2yŒy 1 ; x y 1 ; Œx; ŒŒy 1 ; x ; x i are not Q -equivalent even though their standard complexes have the same simple homotopy type.