New Invariants of Knotoids

In this paper we construct new invariants of knotoids including the odd writhe, the parity bracket polynomial, the affine index polynomial and the arrow polynomial, and give an introduction to the theory of virtual knotoids. The invariants in this paper are defined for classical knotoids in analogy to corresponding invariants of virtual knots. The affine index polynomial and the arrow polynomial provide bounds on the height (minimum crossing distance between endpoints) of a classical knotoid. We show that classical knotoids have symmetric affine index polynomials.