#
Homology Functors With Cubical Bars

##
Volker W. Thuerey

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 cubical 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.

Journal of Homotopy and Related Structures, Vol. 6(2011), No. 1, p. 71-101