Quantum Relatives of Alexander Polynomial

2002/04/24 by Oleg Viro, Viro, Oleg
Mathematics · #17B37 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:17B37 #msc:57M27

paper · pdf · doi:10.48550/arxiv.math/0204290

72 pages

arxiv created 2002/04/24 · arxiv updated 2009/11/30

Abstract

The multivariable Conway function is generalized to oriented framed trivalent graphs equipped with additional structure (coloring). This is done via refinements of Reshetikhin-Turaev functors based on irreducible representations of quantized gl(1|1) and sl(2). The corresponding face state sum models for the generalized Conway function are presented.

Related

• Conway's potential function via the Gassner representation
• A Non-Abelian Generalization of the Alexander Polynomial from Quantum \mathfraksl₃
• On the Conway potential function introduced by Kauffman
• A geometric construction of the Conway potential function
• A topological model for the coloured Alexander invariants