On Habiro's cyclotomic expansions of the Ohtsuki invariant

Ruth Lawrence; Ofer Ron

doi:10.1142/S0218216506004737

On Habiro's cyclotomic expansions of the Ohtsuki invariant

Ruth Lawrence^*, Ofer Ron

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 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.

Original language	English
Pages (from-to)	661-680
Number of pages	20
Journal	Journal of Knot Theory and its Ramifications
Volume	15
Issue number	6
DOIs	https://doi.org/10.1142/S0218216506004737
State	Published - Aug 2006

Bibliographical note

Funding 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.

Keywords

Jones function of a knot
Ohtsuki invariant
State sum expansions

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10.1142/S0218216506004737

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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 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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AU - Ron, Ofer

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AB - 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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On Habiro's cyclotomic expansions of the Ohtsuki invariant

Abstract

Bibliographical note

Keywords

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