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 –punctured sphere visible in the diagram.
Citation
Ryan Blair. David Futer. Maggy Tomova. "Essential surfaces in highly twisted link complements." Algebr. Geom. Topol. 15 (3) 1501 - 1523, 2015. https://doi.org/10.2140/agt.2015.15.1501
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