منابع مشابه
Quandle coloring and cocycle invariants of composite knots and abelian extensions.
Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror can be distinguished by quandle coloring of composite knots. We investigate this and related phenomena. Quandle cocycle invariants are studied in relation t...
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 کاملGeneralized quandle polynomials
We define a family of generalizations of the two-variable quandle polynomial. These polynomial invariants generalize in a natural way to eight-variable polynomial invariants of finite biquandles. We use these polynomials to define a family of link invariants which further generalize the quandle counting invariant.
متن کاملQuandle and Hyperbolic Volume
We show that the hyperbolic volume of a hyperbolic knot is a quandle cocycle invariant. Further we show that it completely determines invertibility and positive/negative amphicheirality of hyperbolic knots.
متن کاملRack 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...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2019
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216519500019