Integral positive (negative) quandle cocycle invariants are trivial for knots (Q260546)

The subject of the paper are two state-sum invariants of knots derived from two kinds of quandle cohomologies: the standard one, referred to as negative quandle cohomology, and a new one, called positive, introduced in an earlier paper [Algebr. Geom. Topol. 15, No. 2, 933--963 (2015; Zbl 1315.57018)] by the authors. The main result is the following: Let \(X\) be a finite quandle and \(\varphi\) either a positive or a negative 2-cocycle for \(X\) over the group of integers. Then the quandle cocycle invariant over \(\varphi\) is trivial, i.e., reduces to quandle coloring, for all knots.