Foundations of geometric cohomology: from co-orientations to product structures
Algebraic Topology
2026-05-01 v3 Geometric Topology
Abstract
This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product of such smooth maps, which provides our geometric cochains with a partially defined product structure inducing the cup product in cohomology. A parallel treatment of homology is also given allowing for a geometric unification of the contravariant and covariant theories.
Keywords
Cite
@article{arxiv.2212.07482,
title = {Foundations of geometric cohomology: from co-orientations to product structures},
author = {Greg Friedman and Anibal M. Medina-Mardones and Dev Sinha},
journal= {arXiv preprint arXiv:2212.07482},
year = {2026}
}
Comments
Preprint, 196 pages, index added. Comments and questions are welcome