Algebraic & Geometric Topology

Positive quandle homology and its applications in knot theory

Zhiyun Cheng and Hongzhu Gao

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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.

Article information

Algebr. Geom. Topol., Volume 15, Number 2 (2015), 933-963.

Received: 16 April 2014
Revised: 18 September 2014
Accepted: 21 September 2014
First available in Project Euclid: 28 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds
Secondary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}

quandle homology positive quandle homology cocycle knot invariant


Cheng, Zhiyun; Gao, Hongzhu. Positive quandle homology and its applications in knot theory. Algebr. Geom. Topol. 15 (2015), no. 2, 933--963. doi:10.2140/agt.2015.15.933.

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