Geometric representations of the homology functor
type: Item
instance of: scholarly article
title: Geometric representations of the homology functor
zbMATH Open document ID: 0936.55003
published in: Ricerche di Matematica
publication date: 1999-05-31T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 55N40
Mathematics Subject Classification ID: 57Q20
zbMATH DE Number: 1293095
zbMATH Keywords: Eilenberg-Steenrod axioms
zbMATH Keywords: manifold classes
author: Sara Dragotti
author: Rosa Esposito
author: Gaetano Magro
author: Lucio Parlato
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1293095