On Habiro's cyclotomic expansions of the Ohtsuki invariant

Ruth Lawrence*, Ofer Ron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)661-680
Number of pages20
JournalJournal of Knot Theory and its Ramifications
Volume15
Issue number6
DOIs
StatePublished - 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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