A Fox-Neuwirth Basis for the Sinha Spectral Sequence
Abstract
Recently, Sinha defined a spectral sequence approximating the (co)homology of the space of long knots in Rm 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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