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.
Paolini, M., Bellettini, G., Beorchia, V., An explicit formula for a Bennequin-type invariant for apparent contours, <<TOPOLOGY AND ITS APPLICATIONS>>, 2009; (156): 747-760. [doi:10.1016/j.topol.2008.09.011] [http://hdl.handle.net/10807/11409]
An explicit formula for a Bennequin-type invariant for apparent contours
Paolini, Maurizio;Bellettini, Giovanni;Beorchia, Valentina
2009
Abstract
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.
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