English

On Usual, Virtual and Welded knotted objects up to homotopy

Geometric Topology 2017-11-30 v3

Abstract

We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a number of results which point out the differences between these various notions. The proofs are mainly based on the techniques of Gauss diagram formulae.

Keywords

Cite

@article{arxiv.1507.00202,
  title  = {On Usual, Virtual and Welded knotted objects up to homotopy},
  author = {Benjamin Audoux and Paolo Bellingeri and Jean-Baptiste Meilhan and Emmanuel Wagner},
  journal= {arXiv preprint arXiv:1507.00202},
  year   = {2017}
}

Comments

14 pages. This paper is an expanded version of a former section, now removed (section 5 in versions 1 and 2) of arXiv:1407.0184. To appear in Journal of the Mathematical Society of Japan

R2 v1 2026-06-22T10:03:43.188Z