|講演者||伊藤 昇氏(茨城工業高等専門学校 国際創造工学科)|
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.