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ON HABIRO'S CYCLOTOMIC EXPANSIONS OF THE OHTSUKI INVARIANT

RUTH LAWRENCE

Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel

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and

OFER RON

Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel

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https://doi.org/10.1142/S0218216506004737Cited by:1 (Source: Crossref)

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.

Keywords:

AMSC: Primary 57M27, Secondary 17B37

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