#### Volume 15, issue 3 (2015)

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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.