University Seminar- Computability, Complexity, and Algebraic Structure: Alternating links on surfaces and hyperbolicity

Time: Wednesday, January 21, 5:00–6:00 pm

Place: Phillips Hall, Room 108

Speaker:  Lecheng Su, Monash University

Title: Alternating links on surfaces and hyperbolicity

Abstract:  In hyperbolic knot theory, we try to find complete hyperbolic structures on knot and link complements. To do so, we often decompose link complements into simpler pieces from the link diagram on a surface. In this talk, we introduce two different ways of decomposing arbitrary knot complements coming from Thurston and Weeks. In the way, we introduce the definition of alternatingness on a nonorientable surface. We obtain hyperbolicity and non-positive curvature results from the combinatorics of the pieces. This is joint work with Jessica Purcell.