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An effective proof of the Cartan formula: Odd primes

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arxiv 2305.08973 v1 pith:MPYVR2IY submitted 2023-05-15 math.AT

Federico Cantero-Morán , Anibal Medina-Mardones This is my paper · ORCID
classification math.AT
keywords formulacartancohomologyactionalgebracoboundarycocyclesconstruct
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abstract

The Cartan formula relates the cup product and the action of the Steenrod algebra on mod~$p$ cohomology. For any pair of mod $p$ cocycles in a simplicial set, where $p$ is an odd prime, we effectively construct a natural coboundary descending to this formula in cohomology.

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  1. Bosonic SPT and invertible phases and its relation to Steenrod's problem

    hep-th 2026-07 accept novelty 7.0 of 10

    Bosonic beyond-cohomology SPT phases are governed by a mod-3 Steenrod-power differential, and a new 6+1-dimensional Z3×Z3 Dijkgraaf-Witten phase is nontrivial on simplicial complexes but trivial on manifolds.

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