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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.22958 |
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| _version_ | 1866915311711682560 |
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| author | Marino, Andrea |
| author_facet | Marino, Andrea |
| contents | 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 à 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Fox-Neuwirth Basis for the Sinha Spectral Sequence Marino, Andrea Algebraic Topology 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 à 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. |
| title | A Fox-Neuwirth Basis for the Sinha Spectral Sequence |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2505.22958 |