Flowing from intersection product to cup product
Algebraic Topology
2021-06-14 v1 Geometric Topology
Abstract
We use a vector field flow defined through a cubulation of a closed manifold to reconcile the partially defined commutative product on geometric cochains with the standard cup product on cubical cochains, which is fully defined and commutative only up to coherent homotopies. The interplay between intersection and cup product dates back to the beginnings of homology theory, but, to our knowledge, this result is the first to give an explicit cochain level comparison between these approaches.
Keywords
Cite
@article{arxiv.2106.05986,
title = {Flowing from intersection product to cup product},
author = {Greg Friedman and Anibal M. Medina-Mardones and Dev Sinha},
journal= {arXiv preprint arXiv:2106.05986},
year = {2021}
}
Comments
26 pages, 7 figures