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Bi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links | | Louis H. Kauffman
; David E. Radford
; | | Date: |
26 Dec 2001 | | Subject: | Geometric Topology; Rings and Algebras MSC-class: 57M25 | math.GT math.RA | | Abstract: | 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. | | Source: | arXiv, math.GT/0112280 | | Services: | Forum | Review | PDF | Favorites | |
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