Algebraic & Geometric Topology

Positive quandle homology and its applications in knot theory

Zhiyun Cheng and Hongzhu Gao

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1511895794

Digital Object Identifier
doi:10.2140/agt.2015.15.933

Mathematical Reviews number (MathSciNet)
MR3342681

Zentralblatt MATH identifier
1315.57018

Subjects
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}

Keywords
quandle homology positive quandle homology cocycle knot invariant

Citation

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. https://projecteuclid.org/euclid.agt/1511895794


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