On homotopy groups of spaces of embeddings of an arc or a circle: the Dax invariant
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911194148765696 |
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| author | Kosanović, Danica |
| author_facet | Kosanović, Danica |
| contents | We compute in many classes of examples the first potentially interesting homotopy group of the space of embeddings of either an arc or a circle into a manifold $M$ of dimension $d\geq4$. In particular, if $M$ is a simply connected 4-manifold the fundamental group of both of these embedding spaces is isomorphic to the second homology group of $M$, answering a question posed by Arone and Szymik. The case $d=3$ gives isotopy invariants of knots in a 3-manifold, that are universal of Vassiliev type $\leq1$, and reduce to Schneiderman's concordance invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_03041 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On homotopy groups of spaces of embeddings of an arc or a circle: the Dax invariant Kosanović, Danica Geometric Topology We compute in many classes of examples the first potentially interesting homotopy group of the space of embeddings of either an arc or a circle into a manifold $M$ of dimension $d\geq4$. In particular, if $M$ is a simply connected 4-manifold the fundamental group of both of these embedding spaces is isomorphic to the second homology group of $M$, answering a question posed by Arone and Szymik. The case $d=3$ gives isotopy invariants of knots in a 3-manifold, that are universal of Vassiliev type $\leq1$, and reduce to Schneiderman's concordance invariant. |
| title | On homotopy groups of spaces of embeddings of an arc or a circle: the Dax invariant |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2111.03041 |