Link diagrams with low Turaev genus
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- by Seungwon Kim PDF
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Abstract:
We classify link diagrams with Turaev genus one and two in terms of an alternating tangle structure of the link diagram. The proof involves surgery along simple loops on the Turaev surface, called cutting loops, which have corresponding cutting arcs that are visible on the planar link diagram. These also provide new obstructions for a link diagram on a surface to come from the Turaev surface algorithm. We also show that inadequate Turaev genus one links are almost-alternating.References
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Additional Information
- Seungwon Kim
- Affiliation: Department of Mathematics, The Graduate Center, CUNY, 365 Fifth Avenue, New York, New York 10016
- Email: skim2@gradcenter.cuny.edu
- Received by editor(s): November 23, 2015
- Received by editor(s) in revised form: October 2, 2016, and February 23, 2017
- Published electronically: October 25, 2017
- Communicated by: Kevin Whyte
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 875-890
- MSC (2010): Primary 57M25
- DOI: https://doi.org/10.1090/proc/13723
- MathSciNet review: 3731718