Rack and quandle homology
نویسنده
چکیده
A rack is a set X equipped with a bijective, self-right-distributive binary operation, and a quandle is a rack which satisfies an idempotency condition. In this paper, we further develop the theory of rack and quandle modules introduced in [8], in particular defining a tensor product ⊗X , the notion of a free X –module, and the rack algebra (or wring) ZX . We then apply this theory to define homology theories for racks and quandles which generalise and encapsulate those developed by Fenn, Rourke and Sanderson[6, 7]; Carter, Elhamdadi, Jelsovsky, Kamada, Langford and Saito [2, 3]; and Andruskiewitsch, Etingof and Graña [1, 4]. AMS Classification numbers Primary: 18G60 Secondary: 18G35, 18E10
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Extensions of Racks and Quandles
A rack is a set equipped with a bijective, self-right-distributive binary operation, and a quandle is a rack which satisfies an idempotency condition. In this paper, we introduce a new definition of modules over a rack or quandle, and show that this definition includes the one studied by Etingof and Graña [9] and the more general one given by Andruskiewitsch and Graña [1]. We further show that ...
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