Higher torsion in 𝐻-spaces

Abstract

This paper is the last of a series of papers investigating the homological structure of //-spaces (see [7; 8; 9; 11]). Here we investigate the consequences of the existence of torsion elements of higher order, that is, elements whose order is divisible by higher powers of p. Again, we investigate the Bockstein spectral sequence Br and prove certain "implication" theorems in it. The techniques of proof are more general than in [7] and [8], and we prove theorems in a more algebraic, abstract context. Thus in 1, we introduce the concept of an //-complex, which one may think of as an abstraction of the chain complex of an //-space. "Implication" theorems for the Bockstein spectral sequences of such //-complexes are proved in 2 and 3. The main results of 3 are Theorems 3.3, 3.11 and 3.12.