Time：15:00-16:00, Tuesday, August 26 2025
Venue: E4-221
Speaker：Takefumi Nosaka, Institute of Science Tokyo
Title: Quandle theory and its applications to knots
Abstract: A quandle is an algebraic system analogous to the conjugacy operation of a group, and is suitable for applications in knot theory. Given a quandle X, Feen-Rourke-Sanderson defined a classifying space BX, whose cohomology is called the rack cohomology. Some topological invariants obtained from a cocycle of BX are called the quandle cocycle invariants. In this talk I will give a survey of quandle (cohomology) and BX, and demonstrate an overview of my results on quandles. For example, I gave some topological invariants (or computations of them) of cup products of knots, cohomology pairing. and closed 3-manifolds etc.
