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2016 Essential twisted surfaces in alternating link complements
Marc Lackenby, Jessica Purcell
Algebr. Geom. Topol. 16(6): 3209-3270 (2016). DOI: 10.2140/agt.2016.16.3209

Abstract

Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface increases in complexity with crossing number. In this paper, we generalize checkerboard surfaces to certain immersed surfaces, called twisted checkerboard surfaces, whose geometry better reflects that of the alternating link in many cases. We describe the surfaces, show that they are essential in the complement of an alternating link, and discuss their properties, including an analysis of homotopy classes of arcs on the surfaces in the link complement.

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Marc Lackenby. Jessica Purcell. "Essential twisted surfaces in alternating link complements." Algebr. Geom. Topol. 16 (6) 3209 - 3270, 2016. https://doi.org/10.2140/agt.2016.16.3209

Information

Received: 11 December 2014; Revised: 23 March 2016; Accepted: 21 April 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1355.57005
MathSciNet: MR3584257
Digital Object Identifier: 10.2140/agt.2016.16.3209

Subjects:
Primary: 57M25

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.16 • No. 6 • 2016
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