Quantum Topology / Hopf Algebra Seminar
Neslihan Gugumcu
National Technical University, Athens, Greece
Knotoids and Their invariants ( joint work with Lou Kauffman)
Abstract: The theory of knotoids, introduced by V.Tureav in 2012, extends the theory of classical knots.
A knotoid is defined in analogy to an open-ended knot diagram, that is, as an image of the unit interval in an
oriented surface under an immersion with finitely many transversal double points endowed with
under/over-data and two distinct endpoints. But for knotoids we allow the endpoints to be in different regions
of the diagram.
In this talk, we first go through the basic notions of knotoids in S^2 and R^2 and review basic notions
from virtual knot theory. We introduce the virtual closure map and show that it is a non-injective
and non-surjective map. We then introduce some invariants of knotoids including the height of a knotoid,
the affine index polynomial and the arrow polynomial. We show both the affine index polynomial and the
arrow polynomial are used to determine the type of a knotoid. We also present a proof for a conjecture by
Turaev, concerning the height of minimal diagrams of knot-type knotoids.
Thursday April 27, 2017 at 2:00 PM in SEO 612