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arXiv · 2212.07482

Foundations of geometric cohomology: from co-orientations to product structures

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

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Greg Friedman, Anibal M. Medina-Mardones, Dev Sinha. 2022-12-14. Foundations of geometric cohomology: from co-orientations to product structures. https://arxiv.org/abs/2212.07482

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