Perturbative invariant of Seifert fibered rational homology spheres associated with trivial first cohomology class (Q1841981)

If the quantum parameter \(q\) is a \(2p\)-th root of unity, \(p\) odd, then the quantum \(SU(2)\) invariant of \(3\)-manifolds admits a refinement involving a modulo \(2\) cohomology class. The author gives a general formula for the \(SU(2)\) invariant of Seifert fibered rational homology spheres over a \(2\)-sphere, equipped with the trivial cohomology class. He can derive the order \(2\) perturbative expansion and obtain some properties for the coefficients of this expansion.