Geodesic
Essential surfaces in highly twisted link complements
Blair, Ryan1 ; Futer, David2 ; Tomova, Maggy3
1Department of Mathematics and Statistics, California State University, Long Beach, 1250 Bellflower Blvd, Long Beach, CA 90840, USA
2Department of Mathematics, Temple University, 1805 North Broad St., Philadelphia, PA 19122, USA
3Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA
Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1501-1523
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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 n–punctured sphere visible in the diagram.

DOI : 10.2140/agt.2015.15.1501
Classification : 57M25, 57M50
Keywords: essential surface, augmented link, hyperbolic link, highly twisted link, twist region, genus bound

Blair, Ryan  1   ; Futer, David  2   ; Tomova, Maggy  3

1 Department of Mathematics and Statistics, California State University, Long Beach, 1250 Bellflower Blvd, Long Beach, CA 90840, USA
2 Department of Mathematics, Temple University, 1805 North Broad St., Philadelphia, PA 19122, USA
3 Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA 
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Blair, Ryan; Futer, David; Tomova, Maggy. Essential surfaces in highly twisted link complements. Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1501-1523. doi: 10.2140/agt.2015.15.1501

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