Topology Seminar- Normalized Yang-Baxter homology and biquandle homotopy invariants

Speaker:Xiao Wang (Jilin University, Changchun, China)
Date and time: Tuesday, January 21, 4:45--6:00pm
Place: 1776 G Street C119
Title: Normalized Yang-Baxter homology and biquandle homotopy invariants
Abstract: .Racks and quandles are special families of solutions to the set-theoretic Yang-Baxter equation. In 2007, R.Fenn, C. Rourke and B. Sanderson constructed rack spaces and homotopy invariants of framed links. In 2011, T. Nosaka built a link invariants using the second homotopy group of the quandle spaces. In this talk, we define a normalized homology for certain family of set-theoretic Yang-Baxter operators. We construct Yang-Baxter spaces for set-theoretic Yang-Baxter operators. Then we build homotopy invariants using the second homotopy group of the Yang-Baxter spaces of biquandles.