arXiv Analytics

Sign in

arXiv:math/0208039 [math.GT]AbstractReferencesReviewsResources

What is a virtual link?

Greg Kuperberg

Published 2002-08-05, updated 2003-06-24Version 2

Several authors have recently studied virtual knots and links because they admit invariants arising from R-matrices. We prove that every virtual link is uniquely represented by a link L in S X I, a thickened, compact, oriented surface S, such that the link complement (S X I) - L has no essential vertical cylinder.

Comments: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-20.abs.html
Journal: Algebr. Geom. Topol. 3 (2003) 587-591
Categories: math.GT
Subjects: 57M25, 57M27, 57M15
Related articles: Most relevant | Search more
arXiv:1604.08386 [math.GT] (Published 2016-04-28)
New presentations of a link and virtual link
arXiv:math/0506393 [math.GT] (Published 2005-06-20, updated 2006-10-16)
Quaternion Algebras and Invariants of Virtual Knots and Links I: The Elliptic Case
arXiv:1011.4640 [math.GT] (Published 2010-11-21, updated 2012-09-02)
A Functorial Map from Virtual Knots to Classical Knots and Generalisations of Parity

Links

Toolbox