Finite-type invariants of knots, links, and graphs. (English) Zbl 0863.57005

The author’s abstract: “We define finite-type invariants for graphs as functionals on certain finite-dimensional vector spaces generated by spatial graphs. These invariants are generalizations of Vassiliev’s knot invariants to links and graphs, but our methods are quite different from those used in his paper. We show how to calculate finite-type invariants. In the case of links, we show a way to relate the invariants on links with different numbers of components, and we generalize a theorem of Birman and Lin to show that the Jones, HOMFLY, and Kauffmann polynomials can be interpreted as sequences of finite-type invariants”.


57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M15 Relations of low-dimensional topology with graph theory
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