Identifications in singular homology theory
Edward R. Fadell · Pacific Journal of Mathematics · 1953
INTRODUCTION 0.1.Given a Mayer complex M, a subcomplex M' is termed an unessential identifier for M if the natural projections from M onto the factor complex M/M' induce isomorphisms-onto on the homology level (see [1, §1.2]).The present paper is a continuation and improvement of certain results obtained by Rado' and Reichelderfer (see [1] and [3]) concerning unessential identifiers for the singular complex R of Rado' (see [1, § 0.1]).We shall make use of the results, terminology, and notation in [1] and [3] with one exception.Because of a conflict in notation in [1] and [3], we shall use the notation η for the homomorphisms η :C S -*C R , ip p p » defined as the trivial homomorphism for p 0 as follows: η p (d 0 , *•• f dp 9 T) = (c?O j ••• > dp, T) (see [1, §0.3]).0.2.The principal results of the present paper may be described as follows.Let N (σp βp ) denote the nucleus of the product homomorphism °pβp ••Cp^Cp THEOREM.The system { N (σ_ β Λ )} is an unessential identifier for R.Furthermore, for each p we have