Special issue: 2014 KOOK-TAPU Workshop on Knot Theory and Related TopicsNo Access

The shadow nature of positive and twisted quandle invariants of knots

Seiichi Kamada

Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

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Victoria Lebed

OCAMI, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

Henri Lebesgue Center, University of Nantes, 2 rue de la Houssinière, BP 92208 F-44322, Nantes Cedex 3, France

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Kokoro Tanaka

Department of Mathematics, Tokyo Gakugei University, 4-1-1 Nukuikita-machi, Koganei-shi, Tokyo 184-8501, Japan

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https://doi.org/10.1142/S0218216515400015Cited by:1 (Source: Crossref)

Abstract

Quandle cocycle invariants form a powerful and well-developed tool in knot theory. This paper treats their variations — namely, positive and twisted quandle cocycle invariants, and shadow invariants. We interpret the former as particular cases of the latter. As an application, several constructions from the shadow world are extended to the positive and twisted cases. Another application is a sharpening of twisted quandle cocycle invariants for multi-component links.

Dedicated to Professor Taizo Kanenobu, Professor Yasutaka Nakanishi, and Professor Makoto Sakuma in celebration of their 60th birthdays.

Keywords:

AMSC: 57M27, 18G60

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