Vassiliev invariants of type one for links in the solid torus

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• 作者：Khaled Bataineh ; Mohammad Abu Zaytoon
• 关键词：Vassiliev invariants ; Solid torus ; Chord diagrams ; Singular links
• 刊名：Topology and its Applications
• 出版年：2010
• 出版时间：1 October 2010
• 年：2010
• 卷：157
• 期：16
• 页码：2495-2504
• 全文大小：213 K

文摘

In Bataineh (2003) [2] we studied the type one invariants for knots in the solid torus. In this research we study the type one invariants for n-component links in the solid torus by generalizing Aicardi's invariant for knots in the solid torus to n-component links in the solid torus. We show that the generalized Aicardi's invariant is the universal type one invariant, and we show that the generalized Aicardi's invariant restricted to n-component links in the solid torus with zero winding number for each component is equal to an invariant we define using the universal cover of the solid torus. We also define and study a geometric invariant for n-component links in the solid torus. We give a lower bound on this invariant using the type one invariants, which are easy to calculate, which helps in computing this geometric invariant, which is usually hard to calculate.