Invariant classes for families of complexes

Fuente: arXiv
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Main Authors: Levin, D., Zuevsky, A.
Format: Preprint
Published: 2024
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author Levin, D.
Zuevsky, A.
author_facet Levin, D.
Zuevsky, A.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2404_09183
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Invariant classes for families of complexes
Levin, D.
Zuevsky, A.
Functional Analysis
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.
title Invariant classes for families of complexes
topic Functional Analysis
url https://arxiv.org/abs/2404.09183