Whitehead Torsion in the CW Category

Abstract

The geometry in Chapter II and the algebraic analysis of Chapter III are synthesized in the definition:

• If (K, L) is a pair of finite, connected CW complexes such that K ↯ L then the torsion of (K, L)—written τ(K, L)—is defined by

  $$ \tau (K,L) = \tau (C(\tilde K,\tilde L)) \in Wh({\pi _1}L) $$

  where (K̃, L̃) is the universal covering of (K,L).