2024/04/14 by Levin, D., Zuevsky, A.
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2404.09183
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.