Positive quandle homology and its applications in knot theory

Abstract

Algebraic homology and cohomology theories for quandles have been studied extensively in recent years. With a given quandle $2$–cocycle ($3$–cocycle) one can define a state-sum invariant for knotted curves (surfaces). In this paper we introduce another version of quandle (co)homology theory, called positive quandle (co)homology. Some properties of positive quandle (co)homology groups are given and some applications of positive quandle cohomology in knot theory are discussed.