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arXiv · 2106.05986

Flowing from intersection product to cup product

Greg Friedman·Anibal M. Medina-Mardones·Dev Sinha
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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.

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Greg Friedman, Anibal M. Medina-Mardones, Dev Sinha. 2021-06-10. Flowing from intersection product to cup product. https://arxiv.org/abs/2106.05986

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