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.
Bibliographical noteFunding Information:
The first author would like to thank Thang Le and Lev Rozansky for many conversations on the subject of computations of 3-manifold invariants. The second author would like to acknowledge partial support from an Excellence Grant from the Hebrew University. The authors would like to thank the referee for helpful comments.
- Jones function of a knot
- Ohtsuki invariant
- State sum expansions