On Virtual Crossing Number Estimates For Virtual Links

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We address the question of detecting minimal virtual diagrams with respect to the number of virtual crossings. This problem is closely connected to the problem of detecting the minimal number of additional intersection points for a generic immersion of a singular link in $R^{2}$. We tackle this problem by the so-called $ξ$-polynomial whose leading (lowest) degree naturally estimates the virtual crossing number. Several sufficient conditions for minimality together with infinite series of new examples are given. We also state several open questions about $M$-diagrams, which are minimal according to our sufficient conditions.
16 Pages, 11 Figures

Keywords

Geometric Topology, 57M25

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/173255

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0811.0712
 http://arxiv.org/abs/0811.0712

Collections

arXiv