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Topology/Geometry Seminar

Right-angled links in thickened surfaces

Rose Kaplan-Kelly (Temple University)

Location:  Online (Click on the Zoom link)
Date & time: Tuesday, 21 February 2023 at 4:00PM - 5:00PM

Alternating links, links which admit a diagram in which crossings alternate between over and under, are traditionally studied with alternating diagrams on S^2 in S^3. In this talk, we will consider links which are alternating on higher genus surfaces S_g in S_g x I. We will 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. In the setting of alternating knots on S^2 in S^3, Gan showed that there are no knots with this property. We will show that an RGCR knot does exist in thickened surfaces.

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