Volume 15, issue 2 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
References
Publication
Received: 16 April 2014
Revised: 18 September 2014
Accepted: 21 September 2014
Published: 22 April 2015
Authors
Zhiyun Cheng
School of Mathematical Sciences
Beijing Normal University
Laboratory of Mathematics and Complex Systems
Ministry of Education
Beijing 100875
China
Hongzhu Gao
School of Mathematical Sciences
Beijing Normal University
Laboratory of Mathematics and Complex Systems
Ministry of Education
Beijing 100875
China