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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Essential surfaces in highly twisted link complements

Ryan Blair, David Futer and Maggy Tomova

Algebraic & Geometric Topology 15 (2015) 1501–1523
Abstract

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.

Keywords
essential surface, augmented link, hyperbolic link, highly twisted link, twist region, genus bound
Mathematical Subject Classification 2010
Primary: 57M25, 57M50
References
Publication
Received: 12 February 2014
Revised: 4 August 2014
Accepted: 11 September 2014
Published: 19 June 2015
Authors
Ryan Blair
Department of Mathematics and Statistics
California State University, Long Beach
1250 Bellflower Blvd
Long Beach, CA 90840
USA
http://www.csulb.edu/~rblair/
David Futer
Department of Mathematics
Temple University
1805 North Broad St.
Philadelphia, PA 19122
USA
http://www.math.temple.edu/~dfuter/
Maggy Tomova
Department of Mathematics
University of Iowa
14 MacLean Hall
Iowa City, IA 52242-1419
USA
http://www.math.uiowa.edu/~mtomova/