Quantum Topology / Hopf Algebra Seminar
Jonathan Schneider
UIC
Three Variants of Welded Knot Theory
Abstract: Welded Knot Theory was originally conceived by Rourke & Fenn in terms of (framed) braids,
and was subsequently expanded by Kauffman, Rourke and Fenn into a quotient of Virtual Knot Theory.
Satoh and Rourke have shown that the theory is modeled by toral surfaces or fiberwise-embedded toral
surfaces. The latter model, however, requires a slight refinement of the the- ory, which we call
“Roto-Welded Knot Theory”. This refinement omits the virtual I-move, and thus represents a partial return
to the original braid concept. In this talk I will compare Welded, Roto-Welded,
and Framed Welded Knot Theories. In particular, only Roto-Welded admits a proven complete
topological model.
Tuesday April 23, 2019 at 3:00 PM in 612 SEO