Pointed quandles of linkoids
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916224691077120 |
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| author | Gügümcü, Neslihan Pflume, Runa |
| author_facet | Gügümcü, Neslihan Pflume, Runa |
| contents | In this paper we define the fundamental quandle of knotoids and linkoids and prove that it is invariant under the under forbidden-move and hence encodes only the information of the underclosure of the knotoid. We then introduce $n$-pointed quandles, which generalize quandles by specifying $n$ elements as ordered basepoints. This leads to the notion of fundamental pointed quandles of linkoids, which enhances the fundamental quandle. Using $2$-pointed quandle allows us to distinguish 1-linkoids with equivalent under-closures and leads to a couple of 1-linkoid invariants. We also generalize the notion of homogeneity of quandles to $n$-homogeneity of quandles. We classify all $\infty$-homogeneous, finite quandles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14083 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pointed quandles of linkoids Gügümcü, Neslihan Pflume, Runa Geometric Topology Quantum Algebra 57K12 In this paper we define the fundamental quandle of knotoids and linkoids and prove that it is invariant under the under forbidden-move and hence encodes only the information of the underclosure of the knotoid. We then introduce $n$-pointed quandles, which generalize quandles by specifying $n$ elements as ordered basepoints. This leads to the notion of fundamental pointed quandles of linkoids, which enhances the fundamental quandle. Using $2$-pointed quandle allows us to distinguish 1-linkoids with equivalent under-closures and leads to a couple of 1-linkoid invariants. We also generalize the notion of homogeneity of quandles to $n$-homogeneity of quandles. We classify all $\infty$-homogeneous, finite quandles. |
| title | Pointed quandles of linkoids |
| topic | Geometric Topology Quantum Algebra 57K12 |
| url | https://arxiv.org/abs/2404.14083 |