Quandle homology groups, their Betti numbers, and virtual knots

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• 作者：Scott Carter ; J. ; Jelsovsky ; Daniel ; Kamada ; Seiichi ; Saito ; Masahico
• 关键词：Primary 55U15 ; 57M25 ; secondary 57M27 ; 55N99
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2001
• 出版时间：March 23, 2001
• 年：2001
• 卷：157
• 期：2-3
• 页码：135-155
• 全文大小：215 K

文摘

Lower bounds for the Betti numbers for homology groups of racks and quandles will be given using the quotient homomorphism to the orbit quandles. Exact sequences relating various types of homology groups are analyzed. Geometric methods of proving non-triviality of cohomology groups are also given, using virtual knots. The results can be applied to knot theory as the first step towards evaluating the state-sum invariants defined from quandle cohomology.