Geometric representations of the homology functor (Q1289512)

This paper can be regarded as a continuation of two papers by the first three authors [Proc. Am. Math. Soc. 120, No. 2, 635-646 (1994; Zbl 0814.55001); Ric. Mat. 39, No. 1, 21-33 (1990; Zbl 0737.57010)]. Assuming the definitions and notations of the above two papers, the authors study in the present paper the question whether or not two different manifold classes may determine the same functor, especially the same homology functor. They also discuss the question whether a minimal condition on a manifold can be found so that it determines a homology functor i.e., satisfies the excision axiom, too. For this, they introduce the ``gluing'' and ``cutting'' properties which are sufficient for the purpose but none of these are necessary conditions. They present examples to establish the last fact and they also determine some weaker condition on a manifold class so that it determines a homology functor.