Vassiliev-Gusarov invariants

Akio Kawauchi
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Akio Kawauchi: Osaka City University, Department of Mathematics

Chapter Chapter 16 in A Survey of Knot Theory, 1996, pp 209-219 from Springer

Abstract: Abstract In this chapter, we discuss a graded Q-algebra of numerical link invariants which we call the Vassiliev-Gusarov invariants (cf. [Vassiliev 1990], [Gusarov 1994, 1994′]). An important observation is that this algebra determines the Jones, skein and Kauffman polynomials and their satellite version invariants, as is discussed in 16.2. In 16.3, we discuss Kontsevich’s iterated integral invariant, and characterize the Vassiliev-Gusarov algebra in terms of the weight systems on chord diagrams. In 16.4, we discuss numerical link invariants which are not of Vassiliev-Gusarov type.

Date: 1996
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DOI: 10.1007/978-3-0348-9227-8_17

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