Geometry of alternating links on surfaces

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We consider links that are alternating on surfaces embedded in a compact 3-manifold. We show that under mild restrictions, the complement of the link decomposes into simpler pieces, generalising the polyhedral decomposition of alternating links of Menasco. We use this to prove various facts about the hyperbolic geometry of generalisations of alternating links, including weakly generalised alternating links described by the first author. We give diagrammatical properties that determine when such links are hyperbolic, find the geometry of their checkerboard surfaces, bound volume, and exclude exceptional Dehn fillings.

Original languageEnglish
Pages (from-to)2349-2397
Number of pages49
JournalTransactions of the American Mathematical Society
Issue number4
Publication statusPublished - 23 Jan 2020

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