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Essential surfaces in
highly twisted link complements
Ryan Blair, David Futer and Maggy Tomova |
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Algebraic & Geometric Topology 15 (2015) 1501–1523
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Abstract |
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We prove that in the complement of a highly twisted link, all closed, essential, meridionally incompressible surfaces must have high genus. The genus bound is proportional to the number of crossings per twist region. A similar result holds for surfaces with meridional boundary: such a surface either has large negative Euler characteristic or is an –punctured sphere visible in the diagram. |
Keywords
essential surface, augmented link, hyperbolic link, highly
twisted link, twist region, genus bound
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Mathematical Subject Classification 2010
Primary: 57M25, 57M50
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References |
Publication
Received: 12 February 2014
Revised: 4 August 2014
Accepted: 11 September 2014
Published: 19 June 2015
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Authors |
| Ryan Blair | |
| Department of Mathematics and
Statistics California State University, Long Beach 1250 Bellflower Blvd Long Beach, CA 90840 USA |
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| http://www.csulb.edu/~rblair/ | |
| David Futer | |
| Department of Mathematics Temple University 1805 North Broad St. Philadelphia, PA 19122 USA |
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| http://www.math.temple.edu/~dfuter/ | |
| Maggy Tomova | |
| Department of Mathematics University of Iowa 14 MacLean Hall Iowa City, IA 52242-1419 USA |
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| http://www.math.uiowa.edu/~mtomova/ | |
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