Directed homological and cohomological operations
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.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Topological and Geometric Data Analysis
Geometric and Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 12 March 2026
- Language
- EN
- Document type
- Preprint