Work

An unknotting invariant for welded knots

Year: 2020

Type: preprint

Abstract: We study a local twist move on welded knots that is an analog of the virtualization move on virtual knots. Since this move is an unknotting operation we define an invariant, unknotting twist number, for welded knots. We relate the unknotting twist number with warping degree and welded unknotting number, and establish a lower bound on the twist number using Alexander quandle coloring. We also study the Gordian distance between welded knots by twist move and define the corresponding Gordian complex.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2008.03479

Authors: Kaur, K., Gill, A., Prabhakar, M., Vesnin, A.

Institutions: Indian Institute of Technology Ropar, National Research Tomsk State University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Department of Science and Technology, Ministry of Science and Technology, India, Russian Science Foundation

Awards: G7327175072, G7749573883, G879902581

OpenAlex ID: W3047914236

Cites: 15

Cited by:

Related to: 10