English

Core groups

Geometric Topology 2025-11-24 v2

Abstract

The core group of a classical link was introduced independently by A.J. Kelly in 1991 and M. Wada in 1992. It is a link invariant defined by a presentation involving the arcs and crossings of a diagram, related to Wirtinger's presentation of the fundamental group of a link complement. Two close relatives of the core group are defined by presentations involving regions rather than arcs; one of them is related to Dehn's presentation of a link group. The definitions are extended to virtual link diagrams and properties of the resulting invariants are discussed.

Cite

@article{arxiv.2311.02048,
  title  = {Core groups},
  author = {Daniel S. Silver and Lorenzo Traldi and Susan G. Williams},
  journal= {arXiv preprint arXiv:2311.02048},
  year   = {2025}
}

Comments

v1: 20 pages, 7 figures. v2: final prepublication version. Further changes may be made before publication in the Journal of Knot Theory and its Ramifications

R2 v1 2026-06-28T13:10:54.074Z