汎用データベース

筑波大学数学談話会

日時 2023年6月1日15時30分~17時00分
場所 オンライン
講演者 伊藤 昇氏(茨城工業高等専門学校 国際創造工学科)
講演題目

A quantization of the Arnold strangeness invariant

概要

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.