Non collapse of the Sinha spectral sequence for knots in R^3

Andrea Marino; Paolo Salvatore

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arXiv · 2504.16785

Non collapse of the Sinha spectral sequence for knots in R^3

Andrea Marino·Paolo Salvatore

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Abstract

We give an explicit description up to the third page of the Sinha homology mod 2 spectral sequence for the space of long knots in $\mathbb{R}^3$, that is conjecturally equivalent to the Vassiliev spectral sequence. The description arises from a multicomplex structure on the Fox Neuwirth chain complexes for euclidean configuration spaces. A computer assisted calculation reveals a non trivial third page differential from a 2-dimensional class, in contrast to the rational case.

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Andrea Marino, Paolo Salvatore. 2025-04-23. Non collapse of the Sinha spectral sequence for knots in R^3. https://arxiv.org/abs/2504.16785

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