arXiv math/05015492005-01math.GTmath.QA

On Habiro's cyclotomic expansions of the Ohtsuki invariant

Ruth Lawrence, Ofer Ron

备注：: LaTeX, 25 pages, 6 figures; updated references and corrected typos
发表信息：: Journal of Knot Theory and its Ramifications 15(6) (2006) 661-680

英文摘要：

We give a self-contained treatment of Le and Habiro's approach to the Jones function of a knot and Habiro's cyclotomic form of the Ohtsuki invariant for manifolds obtained by surgery around a knot. On the way we reproduce a state sum formula of Garoufalidis and Le for the colored Jones function of a knot. As a corollary, we obtain bounds on the growth of coefficients in the Ohtsuki series for manifolds obtained by surgery around a knot, which support the slope conjecture of Jacoby and the first author.

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