Return to search

Flat Virtual Pure Tangles

Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory of interest because its finite-type invariant theory is potentially a topological interpretation of Etingof and Kazhdan's theory of quantization of Lie bi-algebras. Classical knots inject into virtual knots}, and flat virtual knots is the quotient of virtual knots which equates the real positive and negative crossings, and in this sense is complementary to classical knot theory within virtual knot theory.


We classify flat virtual tangles with no closed components and give bases for its ``infinitesimal'' algebras. The classification of the former can be used as an invariant on virtual tangles with no closed components and virtual braids. In a subsequent paper, we will show that the infinitesimal algebras are the target spaces of any universal finite-type invariants on the respective variants of the flat virtual tangles.

Identiferoai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/33962
Date11 December 2012
CreatorsChu, Karene Kayin
ContributorsBar-Natan, Dror
Source SetsUniversity of Toronto
Languageen_ca
Detected LanguageEnglish
TypeThesis

Page generated in 0.0017 seconds