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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Diagrams of Eilenberg-MacLane spaces of any height are formal over Q, implying spectral sequence collapse at page 2 for any diagram over any small category.
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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.
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On formality of diagrams of Eilenberg-MacLane spaces
Diagrams of Eilenberg-MacLane spaces of any height are formal over Q, implying spectral sequence collapse at page 2 for any diagram over any small category.