Non collapse of the Sinha spectral sequence for knots in R^3
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912389034672128 |
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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 |