筑波大学数学談話会

A quantization of the Arnold strangeness invariant

Arnold invariants are celebrated invariants as plane curve versions of Vassiliev knot invariants. Arnold invariants consist of three types. Two of them have been quantized by Viro (1996) and Lanzat-Polyak (2013). In this talk, we quantize the last remaining one, the Arnold strangeness invariant. As a result, we formulate a polynomial invariant expressed as an integral. The quantization is done by integrating the curvature multiplied by an appropriate density. The first term of the Taylor expansion at q=1 corresponds to the rotation number and the second term to the Arnold strangeness invariant.