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arXiv · 2205.10716

Cohomology, Bocksteins, and resonance varieties in characteristic 2

Alexander I. Suciu
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Abstract

We use the action of the Bockstein homomorphism on the cohomology ring $H^*(X,\mathbb{Z}_2)$ of a finite-type CW-complex $X$ in order to define the resonance varieties of $X$ in characteristic 2. Much of the theory is done in the more general framework of the Maurer-Cartan sets and the resonance varieties attached to a finite-type commutative differential graded algebra. We illustrate these concepts with examples mainly drawn from closed manifolds, where Poincar\'e duality over $\mathbb{Z}_2$ has strong implications on the nature of the resonance varieties.

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Alexander I. Suciu. 2022-05-22. Cohomology, Bocksteins, and resonance varieties in characteristic 2. https://doi.org/10.1090/conm%2F790%2F15861

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