Quantum Topology / Hopf Algebra Seminar
Jonathan Schneider
UIC
Three Variants of Welded Knot Theory
Abstract: Continued from Tuesday:
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 theory,
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.
Thursday April 25, 2019 at 3:00 PM in 612 SEO