Homology groups of cubical sets with connections
Algebraic Topology
2018-12-20 v1 Combinatorics
Category Theory
Abstract
Toward defining commutative cubes in all dimensions, Brown and Spencer introduced the notion of "connection" as a new kind of degeneracy. In this paper, for a cubical set with connections, we show that the connections generate an acyclic subcomplex of the chain complex of the cubical set. In particular, our results show that the homology groups of a cubical set with connections are independent of whether we normalize by the connections or we do not, that is, connections do not contribute to any nontrivial cycle in the homology groups of the cubical set.
Cite
@article{arxiv.1812.07600,
title = {Homology groups of cubical sets with connections},
author = {Helene Barcelo and Curtis Greene and Abdul Salam Jarrah and Volkmar Welker},
journal= {arXiv preprint arXiv:1812.07600},
year = {2018}
}