A Fox-Neuwirth Basis for the Sinha Spectral Sequence
Algebraic Topology
2025-05-30 v1
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.
Cite
@article{arxiv.2505.22958,
title = {A Fox-Neuwirth Basis for the Sinha Spectral Sequence},
author = {Andrea Marino},
journal= {arXiv preprint arXiv:2505.22958},
year = {2025}
}