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arXiv · 1810.06505

An axiomatic characterization of Steenrod's cup-$i$ products

Anibal M. Medina-Mardones
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Abstract

We show that any natural construction of cup-$i$ products on the normalized cochains of simplicial sets, parameterized by the minimal free resolution of the trivial $\mathbb{F}_2[\mathbb{S}_2]$-module, is isomorphic---not just homotopic---to Steenrod's original construction if it is non-zero, irreducible, and free. We show that these three conditions are independent, and use them to prove that all cup-$i$ constructions in the literature represent the same isomorphism class.

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Anibal M. Medina-Mardones. 2018-10-15. An axiomatic characterization of Steenrod's cup-$i$ products. https://arxiv.org/abs/1810.06505

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