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Essential twisted
surfaces in alternating link complements
Marc Lackenby and Jessica S Purcell |
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Algebraic & Geometric Topology 16 (2016) 3209–3270
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Abstract |
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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. |
Keywords
alternating links, essential surfaces
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Mathematical Subject Classification 2010
Primary: 57M25
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References |
Publication
Received: 11 December 2014
Revised: 23 March 2016
Accepted: 21 April 2016
Published: 15 December 2016
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Authors |
| Marc Lackenby | |
| Mathematical Institute University of Oxford Radcliffe Observatory Quarter Woodstock Road Oxford OX2 6GG United Kingdom |
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| http://people.maths.ox.ac.uk/lackenby/ | |
| Jessica S Purcell | |
| School of Mathematical
Sciences Monash University 9 Rainforest Walk Room 401 Monash University VIC 3800 Australia |
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| http://users.monash.edu/~jpurcell/ | |
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