منابع مشابه
On the Volume Conjecture for Hyperbolic Knots
In [1], R.M. Kashaev introduced certain invariants of oriented links motivated by his study of quantum dilogarithm functions. Since the classical dilogarithm functions are related to the hyperbolic volumes, he naturally expected that, for hyperbolic knots, the asymptotic behaviors of his invariants determine their volumes, which is in fact confirmed for a few hyperbolic knots by himself in [2]....
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We prove Simon’s conjecture for fibered knots in S: a fibered knot group surjects at most finitely many other knot groups.
متن کاملOn the Volume Conjecture for Cables of Knots
Abstract. We establish the volume conjecture for (m, 2)-cables of the figure 8 knot, when m is odd. For (m, 2)-cables of general knots where m is even, we show that the limit in the volume conjecture depends on the parity of the color (of the Kashaev invariant). There are many cases when the volume conjecture for cables of the figure 8 knot is false if one considers all the colors, but holds tr...
متن کاملOn the AJ conjecture for cables of the figure eight knot
The AJ conjecture relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been verified for some classes of knots, including all torus knots, most double twist knots, (−2, 3, 6n ± 1)-pretzel knots, and most cabled knots over torus knots. In this paper we study the AJ conjecture for (r, 2)-cables of a knot, where r is an odd integer. In particular, we show tha...
متن کاملMorimoto’s Conjecture for M-small Knots
Let X be the exterior of connected sum of knots and Xi the exteriors of the individual knots. In [10] Morimoto conjectured (originally for n = 2) that g(X) < Σ i=1 g(Xi) if and only if there exists a so-called primitive meridian in the exterior of the connected sum of a proper subset of the knots. For m-small knots we prove this conjecture and bound the possible degeneration of the Heegaard gen...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2017
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm148-8-2016