A counterexample to a strong version of the Andrews-Curtis conjecture

Abstract

We prove that the presentations $⟨x,y|[x,y],1⟩$ and $⟨x,y|[x,[x,y^{-1}]{]}^{2}y[y^{-1},x]y^{-1},[x,[[y^{-1},x],x]]⟩$ are not $Q^{\ast }$-equivalent even though their standard complexes have the same simple homotopy type.

7 pages, 1 figure

References in corpus (1)

• The winding invariant

Cited by in corpus (2)

• The winding invariant
• Morse theory for group presentations