Cubes, cacti, and framed long knots
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915481873547264 |
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| author | Koytcheff, Robin Zhang, Yongheng |
| author_facet | Koytcheff, Robin Zhang, Yongheng |
| contents | We define an action of the operad of projective spineless cacti on each stage of the Taylor tower for the space of framed 1-dimensional long knots in any Euclidean space. By mapping a subspace of the overlapping intervals operad to the subspace of normalized cacti, we prove a space-level compatibility of our action with Budney's little 2-cubes action on the space of framed long knots itself. Our result improves upon previous joint work of the first author related to the conjecture that the Taylor tower for classical long knots is a universal Vassiliev invariant over the integers. As a corollary, we reprove the nontriviality of a certain Browder bracket class first detected by Sakai. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08858 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cubes, cacti, and framed long knots Koytcheff, Robin Zhang, Yongheng Algebraic Topology Geometric Topology Primary: 57K10, 57K45, 18F50, 18M75, 55P48. Secondary: 55R80, 57R40 We define an action of the operad of projective spineless cacti on each stage of the Taylor tower for the space of framed 1-dimensional long knots in any Euclidean space. By mapping a subspace of the overlapping intervals operad to the subspace of normalized cacti, we prove a space-level compatibility of our action with Budney's little 2-cubes action on the space of framed long knots itself. Our result improves upon previous joint work of the first author related to the conjecture that the Taylor tower for classical long knots is a universal Vassiliev invariant over the integers. As a corollary, we reprove the nontriviality of a certain Browder bracket class first detected by Sakai. |
| title | Cubes, cacti, and framed long knots |
| topic | Algebraic Topology Geometric Topology Primary: 57K10, 57K45, 18F50, 18M75, 55P48. Secondary: 55R80, 57R40 |
| url | https://arxiv.org/abs/2301.08858 |