Positive quandle homology and its applications in knot theory

Cheng, Zhiyun¹ ; Gao, Hongzhu¹

¹School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Algebraic and Geometric Topology, Tome 15 (2015) no. 2, pp. 933-963

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.933

Classification : 57M25, 57M27, 57Q45
Keywords: quandle homology, positive quandle homology, cocycle knot invariant

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