On ohtsuki’s invariants of integral homology 3-spheres

Abstract

We provide some more explicit formulae to facilitate the computation of Ohtsuki’s rational invariants λn of integral homology 3-spheres extracted from Reshetikhin-TuraevSU(2) quantum invariants. Several interesting consequences will follow from our computation of λ2. One of them says that λ2 is always an integer divisible by 3. It seems interesting to compare this result with the fact shown by Murakami that λ1 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.