#### Volume 15, issue 2 (2015)

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Positive quandle homology and its applications in knot theory

### Zhiyun Cheng and Hongzhu Gao

Algebraic & Geometric Topology 15 (2015) 933–963
##### 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.

##### Keywords
quandle homology, positive quandle homology, cocycle knot invariant
##### Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57Q45