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Essential surfaces in highly twisted link complements

Blair, R
; 
Futer, D
; 
Tomova, M
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Journal Article
Date
2015-06-19
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math.GT
 math.GT
 57M25, 57M50
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http://hdl.handle.net/20.500.12613/5789
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1312.5016v2.pdf
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10.2140/agt.2015.15.1501
Abstract
© 2015, Mathematical Sciences Publishers. All Rights Reserved. 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.
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Mathematical Sciences Publishers
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Algebraic and Geometric Topology
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