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On virtual link invariants

2012/11/15 by Alexander Schrijver, Schrijver, Alexander
Mathematics · #57M27 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.CO #math.GT #math.QA #msc:57M27

paper · pdf · doi:10.48550/arxiv.1211.3572

arxiv created 2012/11/20 · arxiv updated 2012/11/21

Abstract

Virtual links were introduced by Kauffman in 1999. We characterize the virtual link invariants that are partition functions of vertex models (as considered by de la Harpe and Jones), both in the real and in the complex case. We show that for any fixed number of states, these invariants form an affine variety. Basic techniques are the first and second fundamental theorem of invariant theory for the orthogonal group (in the sense of Weyl) and some related methods from algebraic geometry.

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