Whitehead torsion, group extensions, and Zeeman's conjecture in high dimensions

Abstract

WE WORK in the category of finite C W complexes, writing L < K if L is a subcomplex of K, and writing K ~ L if L < K and K deformation retracts to L. The Whitehead group of the group G is denoted Wh(G). If K xt L then r(K, L) E Wh(~'tL) denotes the Whitehead torsion of the pair (K, L). We shall assume a basic knowledge of Whitehead torsion theory. (See [1] or [8] for background material.) The purpose of this paper is to study the problem of realizing Whitehead torsion elements by relative 2-complexes: If ~'o E Wh(rr,L) then we define the dimension of Io by