Explicit chain complexes and spectral sequences compute homology of configuration spaces in positive characteristic, lifting Knudsen's theorem, with a conjecture on twisted coalgebra equivalences implying homotopy invariance.
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Weighted topologies on Ran(M) interpolate Hausdorff and final topologies, equip the latter with a complete uniformity, and are conically stratified when M is Riemannian.
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Homology of configuration spaces in positive characteristic via point-set constructions
Explicit chain complexes and spectral sequences compute homology of configuration spaces in positive characteristic, lifting Knudsen's theorem, with a conjecture on twisted coalgebra equivalences implying homotopy invariance.
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Old and new structures on Ran spaces: Length structures, completeness, and conicality
Weighted topologies on Ran(M) interpolate Hausdorff and final topologies, equip the latter with a complete uniformity, and are conically stratified when M is Riemannian.