Finite CW-complexes

Abstract

Topological spaces of the same homotopy type as CW-complexes are considered (CW-spaces). Construction methods are used to give algebraic characterizations of CW-complexes, firstly of finite type, and secondly, of finite dimension. When both conditions are satisfied, there is an element of the projective class group of the integral group ring of the fundamental group of the space, a homotopy type invariant, whose vanishing is necessary and sufficient to guarantee that a CW-complex be finite.