A Combinatorial Description of the Knot Concordance Invariant Epsilon
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866908284225585152 |
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| author | Dey, Subhankar Doga, Hakan |
| author_facet | Dey, Subhankar Doga, Hakan |
| contents | In this paper, we give a combinatorial description of the concordance invariant $\varepsilon$ defined by Hom in \cite{hom2011knot}, prove some properties of this invariant using grid homology techniques. We also compute $\varepsilon$ of $(p,q)$ torus knots and prove that $\varepsilon(\mathbb{G}_+)=1$ if $\mathbb{G}_+$ is a grid diagram for a positive braid. Furthermore, we show how $\varepsilon$ behaves under $(p,q)$-cabling of negative torus knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_08505 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Combinatorial Description of the Knot Concordance Invariant Epsilon Dey, Subhankar Doga, Hakan Geometric Topology 57K18 (Primary), 57K10 (Secondary) In this paper, we give a combinatorial description of the concordance invariant $\varepsilon$ defined by Hom in \cite{hom2011knot}, prove some properties of this invariant using grid homology techniques. We also compute $\varepsilon$ of $(p,q)$ torus knots and prove that $\varepsilon(\mathbb{G}_+)=1$ if $\mathbb{G}_+$ is a grid diagram for a positive braid. Furthermore, we show how $\varepsilon$ behaves under $(p,q)$-cabling of negative torus knots. |
| title | A Combinatorial Description of the Knot Concordance Invariant Epsilon |
| topic | Geometric Topology 57K18 (Primary), 57K10 (Secondary) |
| url | https://arxiv.org/abs/2010.08505 |