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- W3088332066 abstract "It is known that the writhe calculated from any reduced alternating link diagram of the same (alternating) link has the same value. That is, it is a link invariant if we restrict ourselves to reduced alternating link diagrams. This is due to the fact that reduced alternating link diagrams of the same link are obtainable from each other via flypes and flypes do not change writhe. In this paper, we introduce several quantities that are derived from Seifert graphs of reduced alternating link diagrams. We prove that they are writhe-like invariants in the sense that they are also link invariants among reduced alternating link diagrams. The determination of these invariants are elementary and non-recursive so they are easy to calculate. We demonstrate that many different alternating links can be easily distinguished by these new invariants, even for large, complicated knots for which other invariants such as the Jones polynomial are hard to compute. As an application, we also derive an if and only if condition for a strongly invertible rational link." @default.
- W3088332066 created "2020-10-01" @default.
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- W3088332066 date "2020-09-23" @default.
- W3088332066 modified "2023-10-16" @default.
- W3088332066 title "Writhe-like invariants of alternating links" @default.
- W3088332066 cites W1607742244 @default.
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- W3088332066 doi "https://doi.org/10.48550/arxiv.2009.11381" @default.
- W3088332066 hasPublicationYear "2020" @default.
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