On Habiro's cyclotomic expansions of the Ohtsuki invariant

Ruth Lawrence and Ofer Ron

Abstract: 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 abd Le for the colored Jones function of a knot. As a corollary, we obtain bounds on the growth of coefficients of the Ohtsuki series for manifolds obtained by surgery around a knot, which support the slope conjecture of Jacoby and the first author.

Keywords: knot theory, manifold invariants, Ohtsuki series

AMS subject classification: 57M27 11Z05

Length: 26 pages

Reference: J. Knot Theory Ramificiations 15(2006) no.6 661-680

Last updated April 15th, 2018.
ruthel@math.huji.ac.il