Geometry of alternating links on surfaces

Autor:	Joshua A. Howie, Jessica S. Purcell
Rok vydání:	2020
Předmět:	Applied Mathematics General Mathematics Hyperbolic geometry 010102 general mathematics Geometry 0101 mathematics Link (knot theory) Mathematics::Geometric Topology 01 natural sciences Mathematics Complement (set theory)
Zdroj:	Transactions of the American Mathematical Society. 373:2349-2397
ISSN:	1088-6850 0002-9947
DOI:	10.1090/tran/7929
Popis:	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.
Databáze:	OpenAIRE
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