Peripheral structures of core groups
Geometric Topology
2026-02-26 v2
Abstract
The core group is an invariant of unoriented virtual links. We introduce a peripheral structure for the core group, in which the longitudes are sensitive to orientations. We show that the combination of the core group and its peripheral structure is equivalent, as a link invariant, to the combination of the -orbifold group and its peripheral structure. Examples show that the peripheral structure of the core group can be used to verify noninvertibility of some knots and links.
Cite
@article{arxiv.2504.06365,
title = {Peripheral structures of core groups},
author = {Daniel S. Silver and Lorenzo Traldi},
journal= {arXiv preprint arXiv:2504.06365},
year = {2026}
}
Comments
v1: 24 pages, 5 figures. v2: small edits and a new family of examples. 26 pages, 6 figures