Turaev genus and alternating decompositions

Armond, Cody W; Lowrance, Adam M

doi:10.2140/agt.2017.17.793

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Turaev genus and alternating decompositions

Cody W Armond and Adam M Lowrance

Algebraic & Geometric Topology 17 (2017) 793–830

DOI: 10.2140/agt.2017.17.793

Abstract

We prove that the genus of the Turaev surface of a link diagram is determined by a graph whose vertices correspond to the boundary components of the maximal alternating regions of the link diagram. Furthermore, we use these graphs to classify link diagrams whose Turaev surface has genus one or two, and we prove that similar classification theorems exist for all genera.

Keywords

knot, link, Turaev genus, almost-alternating, alternating decomposition

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 57M27

References

Publication

Received: 9 July 2015

Revised: 15 June 2016

Accepted: 4 August 2016

Published: 14 March 2017

Authors

Cody W Armond
Department of Mathematics Ohio State University at Mansfield 1760 University Drive Mansfield, OH 44906 United States

Adam M Lowrance
Department of Mathematics Vassar College 124 Raymond Ave Box 257 Poughkeepsie, NY 12604 United States

Volume 17, issue 2 (2017)