The Tautness Property of Homology Theory

TL;DR

This paper introduces and investigates the tautness property for Massey homology theory, establishing its equivalence with Kolmogoroff homology on certain spaces, thus extending known properties in cohomology to homology.

Contribution

It defines the tautness property for homology theories and proves the isomorphism between Massey and Kolmogoroff homologies on locally compact, paracompact spaces.

Findings

Massey and Kolmogoroff homologies are isomorphic on specified spaces.

The tautness property is formulated and studied for Massey homology.

The same results apply to Kolmogoroff homology due to the isomorphism.

Abstract

The tautness for a cohomology theory is formulated and studied by various authors. However, the analogous property is not considered for a homology theory. In this paper, we will define and study this very property for the Massey homology theory. Moreover, we will prove that the Kolmogoroff and the Massey homologies are isomorphic on the category of locally compact, paracompact spaces and proper maps. Therefore, we will obtain the same result for the Kolmogoroff homology theory.