Loop homology algebras of polyhedral products decompose as a colimit over the flagification of the defining simplicial complex.
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Minimal resolutions of toric substack structure sheaves are built as deformation retracts of cellular resolutions with explicit combinatorial differentials via the homological perturbation lemma and Moore-Penrose inverses.
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A colimit decomposition for the loop homology of polyhedral products
Loop homology algebras of polyhedral products decompose as a colimit over the flagification of the defining simplicial complex.
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Minimal resolutions of toric substacks by line bundles
Minimal resolutions of toric substack structure sheaves are built as deformation retracts of cellular resolutions with explicit combinatorial differentials via the homological perturbation lemma and Moore-Penrose inverses.