A simplicial version of the 2-dimensional Fulton-MacPherson operad
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866917647778578432 |
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| author | Bottman, Nathaniel |
| author_facet | Bottman, Nathaniel |
| contents | We define an operad in Top, called $\text{FM}_2^W$. The spaces in $\text{FM}_2^W$ come with CW decompositions, such that the operad compositions are cellular. In fact, each space in $\text{FM}_2^W$ is the realization of a simplicial set. We expect, but do not prove here, that $\text{FM}_2^W$ is isomorphic to the 2-dimensional Fulton-MacPherson operad $\text{FM}_2$. Our construction is connected to the author's work on the symplectic $(A_\infty,2)$-category, and suggests a strategy toward equipping the symplectic cochain complex with the structure of a homotopy Batalin-Vilkoviskiy algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_03211 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A simplicial version of the 2-dimensional Fulton-MacPherson operad Bottman, Nathaniel Algebraic Topology Geometric Topology Symplectic Geometry We define an operad in Top, called $\text{FM}_2^W$. The spaces in $\text{FM}_2^W$ come with CW decompositions, such that the operad compositions are cellular. In fact, each space in $\text{FM}_2^W$ is the realization of a simplicial set. We expect, but do not prove here, that $\text{FM}_2^W$ is isomorphic to the 2-dimensional Fulton-MacPherson operad $\text{FM}_2$. Our construction is connected to the author's work on the symplectic $(A_\infty,2)$-category, and suggests a strategy toward equipping the symplectic cochain complex with the structure of a homotopy Batalin-Vilkoviskiy algebra. |
| title | A simplicial version of the 2-dimensional Fulton-MacPherson operad |
| topic | Algebraic Topology Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2101.03211 |