English

On long knots in the full torus

Algebraic Topology 2021-09-16 v2 Group Theory Geometric Topology

Abstract

The aim of this paper is to realise the techniques of picture-valued invariants and invariants valued in free groups for long knots in the full torus. Such knots and links are of a particular interest because of their relation to Legendrian knots, knotoids, 3-manifolds and many other objects. Invariants constructed in the paper are powerful and easy to compare. This paper is a sequel of [6]. Long knots naturally appear in the study of classical knots [1, 8].

Keywords

Cite

@article{arxiv.2104.13820,
  title  = {On long knots in the full torus},
  author = {Sera Kim and Seongjeong Kim and Vassily Olegovich Manturov},
  journal= {arXiv preprint arXiv:2104.13820},
  year   = {2021}
}

Comments

12 pages, 9 figures

R2 v1 2026-06-24T01:36:11.091Z