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FI-hyperhomology and ordered configuration spaces

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arxiv 1903.02722 v2 pith:R6JC4IOI submitted 2019-03-07 math.AT math.RT

classification math.ATmath.RT
keywords stabilityconfigurationresultspacesfi-hyperhomologyorderedrepresentationadapt
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Using a result of Gan and Li on FI-hyperhomology and a semi-simplicial resolution of configuration spaces due to Randal-Williams, we establish an improved representation stability stable range for configuration spaces of distinct ordered points in a manifold. Our bounds on generation degree improve the best known stability slope by a factor of 5/2 in the most general case. We adapt this result of Gan and Li to apply beyond stability arguments involving highly-connected simplicial complexes, and our methods suggest that their result may be widely applicable to improving most stability ranges for FI-modules in the current representation stability literature.

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Cited by 1 Pith paper

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  1. An inductive method for $\mathrm{OI}$-modules

    math.RT 2019-09 accept novelty 7.0 of 10

    An explicit double-exponential upper bound on the regularity of OI-modules presented in finite degrees, together with a new inductive method for proving their structural properties.

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