Bi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

This paper discusses the construction of a generalized Alexander polynomial for virtual knots and links, and the reformulation of this invariant as a quantum link invariant. The algebraic background for the generalized Alexander module is formulated in terms of the biquandle, a generalization of the quandle of David Joyce (which, in turn, is a generalization of the fundamental group of the knot or link). We then introduce the concept of a bi-oriented quantum algebra which provides an algebraic context for the associated quantum invariant.
LaTeX document, 34 pages, 13 figures, in text LaTeX graphics

Keywords

Geometric Topology, Rings and Algebras, 57M25

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/62984

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0112280
 http://arxiv.org/abs/math/0112280

Collections

arXiv