The shadow nature of positive and twisted quandle cocycle invariants of knots

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.

13 pages. In version 2, a new co-author was added, and Section 4 was considerably extended