Finite Type Invariants of w-Knotted Objects: From Alexander to Kashiwara and Vergne

2013/09/27 by Dror Bar-Natan, Bar-Natan, Dror, Zsuzsanna Dancso +1
Mathematics · #57M25 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1309.7155

openalex publication_date 2013/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This preprint was split in two and became the first two parts of a four-part series (arXiv:1405.1956, arXiv:1405:1955, and two in preparation). The remaining relevance of this preprint is due to the series of videotaped lectures (wClips) that are linked within.

Citations

• Integral Expressions for the Vassiliev Knot Invariants
• Vassiliev and Quantum Invariants of Braids
• The lines of the Kontsevich integral and Rozansky's rationality conjecture
• Combinatorial Formulas for Classical Lie Weight Systems on Arrow Diagrams
• Goussarov-Polyak-Viro combinatorial formulas for finite type invariants
• A classifying invariant of knots, the knot quandle
• On Basis-Conjugating Automorphisms of Free Groups
• Wheels, Wheeling, and the Kontsevich Integral of the Unknot

Related

• Finite Type Invariants of w-Knotted Objects IV: Some Computations
• On knot invariants which are not of finite type
• Survey on recent invariants on classical knot theory
• A Representation Theorem for Knots and a Generalization of the Fundamental Theorem of Finite Type Invariants
• Some Dimensions of Spaces of Finite Type Invariants of Virtual Knots