Directed homological and cohomological operations
Algebraic Topology
2026-03-13 v1
Abstract
In this short note, we present a persistence module approach to directed cohomology, dual to the directed homology introduced by the author in a previous article. We lay out the first properties of directed cohomology and in particular of cohomological operations, partially linked to some homological operations. We treat here both the case of a specific class of precubical sets and of general directed spaces.
Cite
@article{arxiv.2603.11967,
title = {Directed homological and cohomological operations},
author = {Eric Goubault},
journal= {arXiv preprint arXiv:2603.11967},
year = {2026}
}