A toric framework on hypercube Vietoris-Rips complexes produces connectivity lower bounds disproving Shukla's conjecture in infinite families, first global coconnectivity upper bounds, and combinatorially realized decomposable cohomology classes answering Adams and Virk.
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New algorithms compute Hom spaces for poset representations in O(n^4 (thick(Y) + thick(Omega^1 Y))^2) time using a uniqueness result for lifts, plus a classical O(n^3 thick(Y)^3) method, both improving on O(n^6) and strengthening AIDA for multiparameter persistence.
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Cohomological properties of the Vietoris--Rips Complex of a Hypercube Graph
A toric framework on hypercube Vietoris-Rips complexes produces connectivity lower bounds disproving Shukla's conjecture in infinite families, first global coconnectivity upper bounds, and combinatorially realized decomposable cohomology classes answering Adams and Virk.