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arXiv · 2505.22958

A Fox-Neuwirth Basis for the Sinha Spectral Sequence

Andrea Marino
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Abstract

Recently, Sinha defined a spectral sequence approximating the (co)homology of the space of long knots in R^m modulo immersions, stemming from a cosimplicial structure on the compactified configuration spaces \`a la Kontsevich. We provide an equivalent cosimplicial structure on (the barycentric subdivision of) a regular CW complex with cells indexed by Fox-Neuwirth trees. As a corollary, we give a combinatorial presentation of the Sinha Spectral Sequence in terms of Fox-Neuwirth trees for all dimensions m>=2 and all coefficients.

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Andrea Marino. 2025-05-29. A Fox-Neuwirth Basis for the Sinha Spectral Sequence. https://arxiv.org/abs/2505.22958

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