BIMSA > BIMSA Topology Seminar BIMSA Topology Seminar Residual finiteness of fundamental n-quandles of links
Residual finiteness of fundamental n-quandles of links
Organizers
Matthew Burfitt , Jingyan Li , Pravin Kumar , Jie Wu
Speaker
Neeraj K. Dhanwani
Time
Thursday, April 16, 2026 3:00 PM - 4:00 PM
Venue
A3-4-301
Online
Zoom 518 868 7656 (BIMSA)
Abstract
A quandle is an algebraic system with a binary operation satisfying three axioms that are algebraic formulations of the three Reidemeister moves of planar diagrams of links in 3-space. We start our talk with a definition and some examples of a quandle. In this talk, we will define residual finiteness properties on quandles and discuss their implications. We will prove that the fundamental n-quandle of any link in the 3-sphere is residually finite for each $n \geq 2$. This supplements the recent result on residual finiteness of link quandles and the classification of links whose fundamental n-quandles are finite for some n. If time permits, we also discuss several general results on these finiteness properties and on many families of quandles that admit them.