RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
Forthcoming seminars
Seminar calendar
List of seminars
Archive by years
Register a seminar

Search
RSS
Forthcoming seminars





You may need the following programs to see the files








Knots and Representation Theory
April 30, 2013 16:30, Moscow
 


Virtual Knots and Fibered Knots

M. Chrisman

Monmouth University

Number of views:
This page:65

Abstract: Let $L=J \sqcup K$ be a two component link in $S^3$ such that $J$ is a fibered knot and the linking number of $J$ and $K$ is zero. Let $\mathscr{FL}$ denote the ambient isotopy classes of such links $L$ and let $\mathscr{VK}$ denote the set of virtual isotopy classes of virtual knots. We construct a surjective map $\Gamma: \mathscr{FL} \to \mathscr{VK}$. The map is used to give applications of virtual knot theory to classical knot theory. We use virtual knot invariants to distinguish classical two component links, detect non-invertibility of two component classical links, and establish minimality theorems for diagrams of classical two component links. The examples reveal that subtle geometric properties of classical knots can be detected easily using virtual knot theory.

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020