Liftings of knots in $S_{g} \times S^{1}$ and covering of virtual knots
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917754685095936 |
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| author | Kim, Seongjeong |
| author_facet | Kim, Seongjeong |
| contents | A virtual link diagram is called {\em (mod $m$) almost classical} if it admits a (mod $m$) Alexander numbering. In \cite{BodenGaudreauHarperNicasWhite}, it is shown that Alexander polynomial for almost classical links can be defined by using the homology of the associated infinite cyclic cover. On the other hand, in \cite{NaokoKamada} an infinite family of $m$ fold covering over a virtual knot is constructed so that it is mod $m$ almost classical link for all $m$ by using oriented cut point. In this paper, another way to obtain a family of $m$-fold coverings over a given virtual knots, which are mod $m$ almost classical, by using knots in $S_{g} \times S^{1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09583 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Liftings of knots in $S_{g} \times S^{1}$ and covering of virtual knots Kim, Seongjeong Geometric Topology 57K10, 57K12 A virtual link diagram is called {\em (mod $m$) almost classical} if it admits a (mod $m$) Alexander numbering. In \cite{BodenGaudreauHarperNicasWhite}, it is shown that Alexander polynomial for almost classical links can be defined by using the homology of the associated infinite cyclic cover. On the other hand, in \cite{NaokoKamada} an infinite family of $m$ fold covering over a virtual knot is constructed so that it is mod $m$ almost classical link for all $m$ by using oriented cut point. In this paper, another way to obtain a family of $m$-fold coverings over a given virtual knots, which are mod $m$ almost classical, by using knots in $S_{g} \times S^{1}$. |
| title | Liftings of knots in $S_{g} \times S^{1}$ and covering of virtual knots |
| topic | Geometric Topology 57K10, 57K12 |
| url | https://arxiv.org/abs/2309.09583 |