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arXiv · 1903.02722

FI-hyperhomology and ordered configuration spaces

Jeremy Miller·Jennifer C. H. Wilson
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Abstract

Using a result of Gu\`es on FI-hyperhomology (a variant of a result of Gan-Li) and a semi-simplicial resolution of configuration spaces due to Kupers-Miller-Tran, we establish an explicit stable range for cohomological representation stability for configuration spaces of distinct ordered points in a manifold. Our bounds on generation degree were a factor of 5/2 better than those previously established at the time this paper was first posted. This updated article replaces an older version, which contained a mistake pointed out to us by Nicolas Gu\`es. We are grateful to Gu\`es for identifying the error and suggesting the resolution.

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Jeremy Miller, Jennifer C. H. Wilson. 2019-03-07. FI-hyperhomology and ordered configuration spaces. https://arxiv.org/abs/1903.02722

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