Abstract
We calculate the Ohtsuki invariants [Formula: see text] [Formula: see text] of every Brieskorn–Hamm manifold [Formula: see text] which is a rational homology [Formula: see text]-sphere. We denote the order of [Formula: see text] by [Formula: see text]. By the result, we show that the third Ohtsuki invariant [Formula: see text] of the Brieskorn–Hamm manifolds [Formula: see text] with [Formula: see text] is negative, and the third Ohtsuki invariant [Formula: see text] of most Brieskorn–Hamm manifolds [Formula: see text] with [Formula: see text] is positive.
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