Geometry MMA Seminar: Counting and classifying right-angled links in thickened surfaces

Speaker:   Rose Kaplan-Kelly, George Mason University

Title:   Counting and classifying right-angled links in thickened surfaces

Abstract:  An overarching question in knot theory is that of how much we can learn about a link's complement from the link's diagrams. Alternating links, links which admit diagrams in which crossings alternate between over and under, have been especially useful towards addressing this question.  In this talk, we will consider a generalization of alternating links and their complements in thickened surfaces. In particular, a family of generalized alternating links that correspond to Euclidean and hyperbolic tilings and have a right-angled complete hyperbolic structure on their complements. We will find an upper bound on the number of these links for each genus g projection surface and consider the commensurability classes of their complements. 

Time: Monday, February 12, 2024 – 10:30am-11:30am

Place: Exploratory Hall, Room 4106