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

Fuente: arXiv
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Autori principali: Marino, Andrea, Salvatore, Paolo
Natura: Preprint
Pubblicazione: 2025
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author Marino, Andrea
Salvatore, Paolo
author_facet Marino, Andrea
Salvatore, Paolo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_16785
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Non collapse of the Sinha spectral sequence for knots in R^3
Marino, Andrea
Salvatore, Paolo
Algebraic Topology
Geometric Topology
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.
title Non collapse of the Sinha spectral sequence for knots in R^3
topic Algebraic Topology
Geometric Topology
url https://arxiv.org/abs/2504.16785