Fiedler type combinatorial formulas for generalized Fiedler type invariants of knots in M

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• 作者：S.A. Grishanov ; V.A. Vassiliev
• 关键词：Knot invariant ; Weight system ; Gauss diagram ; Combinatorial formula
• 刊名：Topology and its Applications
• 出版年：2009
• 出版时间：15 August 2009
• 年：2009
• 卷：156
• 期：14
• 页码：2307-2316
• 全文大小：327 K

文摘

We construct combinatorial formulas of Fiedler type (i.e. composed of oriented Gauss diagrams arranged by homotopy classes of loops in the base manifold, see [T. Fiedler, Gauss Diagram Invariants for Knots and Links, Math. Appl., vol. 552, Kluwer Academic Publishers, 2001; M. Polyak, O. Viro, Gauss diagram formulas for Vassiliev invariants, Int. Math. Res. Not. 11 (1994) 445–453]) for an infinite family of finite type invariants of knots in M²×R¹ (M² orientable), introduced in [S.A. Grishanov, V.A. Vassiliev, Two constructions of weight systems for invariants of knots in non-trivial 3-manifolds, Topology Appl. 155 (2008) 1757–1765].