Brunnian links and Kontsevich graph complex I
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866909988668047360 |
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| author | Botvinnik, Boris Watanabe, Tadayuki |
| author_facet | Botvinnik, Boris Watanabe, Tadayuki |
| contents | We construct a natural chain map from the Kontsevich graph complex to the rational singular chain complex of $B\mathrm{Diff}_\partial(D^{2k})$ when the dimension $2k$ is sufficiently large, generalizing Goussarov and Habiro's theories of surgery on 3-valent graphs in 3-manifolds. Our construction can be considered as a topological realization of the Kontsevich graph complex. We also give new constructions of elements in the rational homotopy groups of $B\mathrm{Diff}_\partial(D^{2k})$ which are determined by well-known cycles in the graph complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08200 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Brunnian links and Kontsevich graph complex I Botvinnik, Boris Watanabe, Tadayuki Geometric Topology Algebraic Topology 57R50, 57Q45, 55Q15, 55R40, 57R65 We construct a natural chain map from the Kontsevich graph complex to the rational singular chain complex of $B\mathrm{Diff}_\partial(D^{2k})$ when the dimension $2k$ is sufficiently large, generalizing Goussarov and Habiro's theories of surgery on 3-valent graphs in 3-manifolds. Our construction can be considered as a topological realization of the Kontsevich graph complex. We also give new constructions of elements in the rational homotopy groups of $B\mathrm{Diff}_\partial(D^{2k})$ which are determined by well-known cycles in the graph complex. |
| title | Brunnian links and Kontsevich graph complex I |
| topic | Geometric Topology Algebraic Topology 57R50, 57Q45, 55Q15, 55R40, 57R65 |
| url | https://arxiv.org/abs/2601.08200 |