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- W4226368942 abstract "Traditionally, alternating links are studied with alternating diagrams on $S^2$ in $S^3$. In this paper, we consider links which are alternating on higher genus surfaces $S_g$ in $S_g times I$. We define what it means for such a link to be right-angled generalized completely realizable (RGCR) and show that this property is equivalent to the link having two totally geodesic checkerboard surfaces, equivalent to each checkerboard surface consisting of one type of polygon, and equivalent to a set of restrictions on the link's alternating projection diagram. We then use these diagram restrictions to classify RGCR links according to the polygons in their checkerboard surfaces and provide a bound on the number of RGCR links for a given surface of genus $g$. Along the way, we answer a question posed by Champanerkar, Kofman, and Purcell about links with alternating projections on the torus." @default.
- W4226368942 created "2022-05-05" @default.
- W4226368942 creator A5090328780 @default.
- W4226368942 date "2022-03-16" @default.
- W4226368942 modified "2023-09-26" @default.
- W4226368942 title "Right-angled links in thickened surfaces" @default.
- W4226368942 doi "https://doi.org/10.48550/arxiv.2203.08963" @default.
- W4226368942 hasPublicationYear "2022" @default.
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