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Positive quandle
homology and its applications in knot theory
Zhiyun Cheng and Hongzhu Gao |
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Algebraic & Geometric Topology 15 (2015) 933–963
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Abstract |
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Algebraic homology and cohomology theories for quandles have been studied extensively in recent years. With a given quandle –cocycle (–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
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57Q45
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References |
Publication
Received: 16 April 2014
Revised: 18 September 2014
Accepted: 21 September 2014
Published: 22 April 2015
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Authors |
| Zhiyun Cheng | |
| School of Mathematical
Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China |
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| Hongzhu Gao | |
| School of Mathematical
Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China |
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