Classifying links under fused isotopy

2006/06/08 by Andrew Fish, Fish, Andrew, Ebru Keyman +1
Computer Science · Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #User Authentication and Security Systems #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0606198

6 pages, 6 figures

arxiv created 2006/06/08 · openalex publication_date 2006/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

All knots are fused isotopic to the unknot via a process known as virtualization. We extend and adapt this process to show that, up to fused isotopy, classical links are classified by their linking numbers.

Related

• Diagrams realizing prescribed sublink diagrams for virtual links and welded links
• A new classification of links and some calculations using it
• Virtual, Welded, and Ribbon Links in Arbitrary Dimensions
• Is every knot isotopic to the unknot?
• A 1-parameter approach to links in a solid torus