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Link diagrams with low Turaev genus


Author: Seungwon Kim
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 57M25
DOI: https://doi.org/10.1090/proc/13723
Published electronically: October 25, 2017
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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.


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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

DOI: https://doi.org/10.1090/proc/13723
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
Article copyright: © Copyright 2017 American Mathematical Society