Turaev genus and alternating decompositions

Armond, Cody W¹ ; Lowrance, Adam M²

¹Department of Mathematics, Ohio State University at Mansfield, 1760 University Drive, Mansfield, OH 44906, United States
²Department of Mathematics, Vassar College, 124 Raymond Ave Box 257, Poughkeepsie, NY 12604, United States

Algebraic and Geometric Topology, Tome 17 (2017) no. 2, pp. 793-830

Résumé

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.

Détail

DOI : 10.2140/agt.2017.17.793

Classification : 57M25, 57M27
Keywords: knot, link, Turaev genus, almost-alternating, alternating decomposition

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