An explicit formula for a Bennequin-type invariant of apparent contours

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• 作者：Giovanni Bellettini ; Valentina Beorchia ; Maurizio Paolini
• 关键词：Apparent contour ; Vassiliev-type invariants ; Bennequin invariant
• 刊名：Topology and its Applications
• 出版年：2009
• 出版时间：1 February 2009
• 年：2009
• 卷：156
• 期：4
• 页码：747-760
• 全文大小：301 K

文摘

We derive an explicit formula for the computation of a Vassiliev-type invariant of an apparent contour introduced recently by Ohmoto and Aicardi using appropriate linking numbers of its Legendrian lift. Our formula does not require the construction of the Legendrian lift and only takes into account the nodes, the cusps, the extremal points and the orientation of the apparent contour. In this way the computation can be implemented into a computer program; we demonstrate its use with some examples.