Simple homotopy type of finite 2-complexes with finite abelian fundamental group

Abstract

Theorem 1. Let K K be a finite 2 2 -dimensional C W CW -complex with π 1 ( K ) {\pi _1}(K) finite and abelian. Then every element of the Whitehead group of K K is realizable as the torsion of a self-homotopy equivalence on K K . Theorem 2. Homotopy equivalence and simple homotopy equivalence are the same for finite 2 2 -dimensional C W CW -complexes with finite abelian fundamental groups.