Homology Functors with Cubical Bars
K-Theory and Homology
2014-02-17 v4 Algebraic Topology
Abstract
This work arose from efforts to generalise the usual cubical boundary by using different 'weights' for opposite faces, but still to obtain a chain complex, and this method was found to generalise. We describe a variant of the classical singular homology theory, in which the usual boundary (n-1)-cubes of each n-cube are replaced by combinations of internal (n-1)-cubes parallel to the boundary. This defines a generalised homology theory, but the usual singular homology can be recovered by taking the quotient by the degenerate singular cubes.
Cite
@article{arxiv.math/0605156,
title = {Homology Functors with Cubical Bars},
author = {Volker W. Thürey},
journal= {arXiv preprint arXiv:math/0605156},
year = {2014}
}
Comments
31 pages, 4 figures; new title; better display; unchanged results