An Alexander polynomial for MOY graphs
| Autor: | Bao, Yuanyuan, Wu, Zhongtao |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| Popis: | We introduce an Alexander polynomial for MOY graphs. For a framed trivalent MOY graph $\mathbb{G}$, we refine the construction and obtain a framed ambient isotopy invariant $\Delta_{(\mathbb{G},c)}(t)$. The invariant $\Delta_{(\mathbb{G}, c)}(t)$ satisfies a series of relations, which we call MOY-type relations, and conversely these relations determine $\Delta_{(\mathbb{G}, c)}(t)$. Using them we provide a graphical definition of the Alexander polynomial of a link. Finally, we discuss some properties and applications of our invariants. Comment: This version is accepted for publication in Selecta Mathematica. We thank the referee for careful reading and many helpful comments |
| Databáze: | arXiv |
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