arXiv:0907.0172 Abstract | arXiv Analytics

arXiv:0907.0172 [math.GT]Abstract References Reviews Resources

On the Volume Conjecture for Cables of Knots

Published 2009-07-01, updated 2009-08-20Version 3

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 true if one restricts the colors to a subset of the set of positive integers.

Comments: Corrected proof of Lemma 4.5. Accepted to publish in JKTR

Categories: math.GT, math.QA

Subjects: 57N10, 57M25

Keywords: volume conjecture depends, kashaev invariant, general knots, holds true

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