On relative homotopy groups of modules
type: Item
instance of: scholarly article
title: On relative homotopy groups of modules
zbMATH Open document ID: 1147.55009
DOI: 10.1155/2007/27626
author: C. Joanna Su
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-06-03T00:00:00Z
full work available at URL: https://eudml.org/doc/54618
review text: Summary: In his book [Homotopy Theory and Duality, London: Thomas Nelson and Sons (1967; Zbl 0155.50801)], \textit{P. Hilton} described the concepts of relative homotopy theory in module theory. We study in this paper the possibility of parallel concepts of fibration and cofibration in module theory, analogous to the existing theorems in algebraic topology. First, we discover that one can study relative homotopy groups, of modules, from a viewpoint which is closer to that of (absolute) homotopy groups. Then, through the study of various cases, we learn that the classic fibration/cofibration relation does not come automatically. Nonetheless, the ability to see the relative homotopy groups as absolute homotopy groups, in a stronger sense, promises to justify our ultimate search.
Mathematics Subject Classification ID: 55P99
Mathematics Subject Classification ID: 16D99
zbMATH DE Number: 5282537
MaRDI profile type: Publication
OpenAlex ID: W2087785071
cites work: The category of long exact sequences and the homotopy exact sequence of modules
cites work: Some examples of nontrivial homotopy groups of modules
description: scientific article; zbMATH DE number 5282537