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.