BIMSA > BIMSA Topology Seminar BIMSA Topology Seminar Virtual models and quantum invariants of projective knots
Virtual models and quantum invariants of projective knots
Organizers
Matthew Burfitt , Jingyan Li , Pravin Kumar , Jie Wu
Speaker
Visakh Narayanan
Time
Thursday, May 7, 2026 3:00 PM - 4:15 PM
Venue
A3-4-312
Online
Zoom 361 038 6975 (BIMSA)
Abstract
It is shown that the theory of virtual knots can be employed to construct a model for knots in projective space. Through this new perspective, one would like to see which of the invariants of virtual knots can be transformed to invariants of projective knots. We show that most of the quantum invariants of virtual knots descend to invariants of projective knots through this model. We first construct a model for the Jones polynomial and obtain a condition for checking affineness of a projective knot. There are multiple models of Khovanov homology for virtual knots. Manturov constructed a model which was re-interpreted by Dye, Kaestner and Kauffman. We will see that this model provides a homology theory for projective knots.