Embedding spaces of split links
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916657345069056 |
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| author | Boyd, Rachael Bregman, Corey |
| author_facet | Boyd, Rachael Bregman, Corey |
| contents | We study the homotopy type of the space $E(L)$ of unparametrised embeddings of a split link $L=L_1\sqcup \ldots \sqcup L_n$ in $\mathbb{R}^3$. Our main result is a simple description of the fundamental group, or motion group, of $E(L)$, and we extend this to a description of the motion group of embeddings in $S^3$. The main tool we build is a semi-simplicial space of separating systems, which we show is homotopy equivalent to $E(L)$. This combinatorial object provides a gateway to studying the homotopy type of $E(L)$ via the homotopy type of the spaces $E(L_i)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_00619 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Embedding spaces of split links Boyd, Rachael Bregman, Corey Geometric Topology Algebraic Topology Group Theory 58D10, 55P15, 55U10, 20F34 (primary), 57M07, 20F36 (secondary) We study the homotopy type of the space $E(L)$ of unparametrised embeddings of a split link $L=L_1\sqcup \ldots \sqcup L_n$ in $\mathbb{R}^3$. Our main result is a simple description of the fundamental group, or motion group, of $E(L)$, and we extend this to a description of the motion group of embeddings in $S^3$. The main tool we build is a semi-simplicial space of separating systems, which we show is homotopy equivalent to $E(L)$. This combinatorial object provides a gateway to studying the homotopy type of $E(L)$ via the homotopy type of the spaces $E(L_i)$. |
| title | Embedding spaces of split links |
| topic | Geometric Topology Algebraic Topology Group Theory 58D10, 55P15, 55U10, 20F34 (primary), 57M07, 20F36 (secondary) |
| url | https://arxiv.org/abs/2207.00619 |