On Ohtsuki's invariants of integral homology 3-spheres, I

Abstract

An attempt is made to conceptualize the derivation as well as to facilitate the computation of Ohtsuki's rational invariants ${\lambda }_n$ of integral homology 3-spheres extracted from Reshetikhin-Turaev SU(2) quantum invariants. Several interesting consequences will follow from our computation of ${\lambda }_2$. One of them says that ${\lambda }_2$ is always an integer divisible by 3. It seems interesting to compare this result with the fact shown by Murakami that ${\lambda }_1$ is 6 times the Casson invariant. Other consequences include some general criteria for distinguishing homology 3-spheres obtained from surgery on knots by using the Jones polynomial.

arXiv comment35 pages, amslatex, no figures. Some minor changes are made, including the strengthening of the conclusion of Theorem 1.2 and the reformulation of Conjecture 4.1

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