Positive quandle homology and its applications in knot theory

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.

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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

Volume 15, issue 2 (2015)

Zhiyun Cheng and Hongzhu Gao

Abstract