Friday Seminar on Knot Theory(2019年度)

組織委員 岡崎 真也・河村 建吾・滝岡 英雄

日時 2019月4月12日(金)16:00~17:00
講演者(所属) 清水理佳(群馬工業高等専門学校)
タイトル The warping sum of knots
場所 理学部 F棟 415号室(中講究室)
アブストラクト An oriented knot diagram is said to be monotone if one can travel along the diagram so that one meets each crossing as an over-crossing first starting at a point on the diagram. The warping degree of an oriented knot diagram is the minimum number of crossing-changes which are required to obtain a monotone diagram from the knot diagram. For an unoriented knot diagram, the warping sum is the value of the sum of the warping degrees with both orientations. We define the warping sum of an unoriented knot to be the minimal value of the warping sum for all minimal-crossing diagrams of the knot. It has been shown that the warping sum is less than or equal to the crossing number minus one for any knot, and the equality holds if and only if the knot is prime and alternating. We also define a knot invariant, the reduced warping sum of a knot, to be the minimal value of the warping sum for all diagrams of the knot. In this talk, we determine knots with warping sum and reduced warping sum three or less. This is a joint work with Slavik Jablan.
最終更新日: 2019年3月22日