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arXiv · 2404.09183

Invariant classes for families of complexes

D. Levin·A. Zuevsky
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Abstract

We consider families of chain-cochain infinite complexes $\mathcal C$ of spaces with elements depending on a number of parameters, and endowed with a converging associative multiple product. The existence of left/right local/non-local square-vanishing ideals is assumed for subspaces of $\mathcal C$-spaces. We show that a set of differential and orthogonality relations together with coherence conditions on indices of a chain-cochain complex $\mathcal C$ elements generates families of graded differential algebras. With the appropriate orthogonality conditions on completions of $\mathcal C$ elements in the multiple product, we define the equivalence classes of cohomology invariants.

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D. Levin, A. Zuevsky. 2024-04-14. Invariant classes for families of complexes. https://arxiv.org/abs/2404.09183

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