منابع مشابه
Rack and quandle homology
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 ho...
متن کاملCocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology
Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Graña. We specialize that theory to the case when there is a group action on the coefficients. First, quandle modules are used to generalize Burau representations and Alexander modules for classical knots. Second, 2-cocycles valued in non-abelian groups are us...
متن کاملYang–baxter Deformations and Rack Cohomology
Abstract. In his study of quantum groups, Drinfeld suggested to consider set-theoretic solutions of the Yang–Baxter equation as a discrete analogon. As a typical example, every conjugacy class in a group, or more generally every rack Q provides such a Yang–Baxter operator cQ : x ⊗ y 7→ y ⊗ x . In this article we study deformations of cQ within the space of Yang–Baxter operators. Over a complete...
متن کاملThe Cohomology Algebra of a Subalgebra of the Steenrod Algebra
We compute the cohomology algebra of P (1), the subalgebra of the Steenrod algebra generated by P 1 and P p. This completes a partial result given by Arunas Liulevicius in 1962 and provides explicit representatives in the cobar construction for all but one of the algebra generators.
متن کامل2 9 Ja n 20 02 ON RACK COHOMOLOGY
We prove that the lower bounds for Betti numbers of the rack, quandle and degeneracy cohomol-ogy given in [CJKS] are in fact equalities. We compute as well the Betti numbers of the twisted cohomology introduced in [CES]. We also give a group-theoretical interpretation of the second cohomology group for racks.
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2011
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216511010073