2019/05/10 by Neslihan Gügümcü, Louis H. Kauffman, Gügümcü, Neslihan +1
Mathematics · Medicine · #57M20 #57M27 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1905.04089
openalex publication_date 2019/05/10 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
This paper investigates the parity concept in knotoids in S2 and in ℝ2 in relation with virtual knots. We show that the virtual closure map is not surjective and give specific examples of virtual knots that are not in the image. We introduce a planar version of the parity bracket polynomial for knotoids in ℝ2. By using the Nikonov/Manturov theorem on minimal diagrams of virtual knots we prove a conjecture of Turaev showing that minimal diagrams of knot-type knotoids have zero height.