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