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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Geometry of alternating links on surfaces


Authors: Joshua A. Howie and Jessica S. Purcell
Journal: Trans. Amer. Math. Soc. 373 (2020), 2349-2397
MSC (2010): Primary 57M27, 57M20
DOI: https://doi.org/10.1090/tran/7929
Published electronically: January 23, 2020
MathSciNet review: 4069222
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Abstract: 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.


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Additional Information

Joshua A. Howie
Affiliation: School of Mathematical Sciences, Monash University, Victoria 3800, Australia
Address at time of publication: Department of Mathematics, University of California, Davis, Davis, California 95616
Email: josh.howie@monash.edu

Jessica S. Purcell
Affiliation: School of Mathematical Sciences, Monash University, Victoria 3800, Australia
MR Author ID: 807518
ORCID: 0000-0002-0618-2840
Email: jessica.purcell@monash.edu

Received by editor(s): December 6, 2018
Received by editor(s) in revised form: June 5, 2019
Published electronically: January 23, 2020
Additional Notes: The first author was supported by a Lift-off Fellowship from the Australian Mathematical Society.
Both authors were partially supported by grants from the Australian Research Council.
Article copyright: © Copyright 2020 American Mathematical Society