Quantum \(SU(2)\)-invariants for three-manifolds associated with nontrivial cohomology classes modulo two (Q2725556)

This work is a continuation of the author's paper [Contemp. Math. 233, 117-136 (1999; Zbl 0929.57009)]. From the text: ``Let \(p\) be an odd prime and \(M\) a \({\mathbb Z/p}\mathbb Z\)-homology three-sphere. For a cohomology class \(\theta\in H^1(M;{\mathbb Z/p}\mathbb Z)\), let \(\tau^{SU(2)}_{2p}(M,\theta)\) be the quantum \(SU(2)\)-invariant with level \(2p-2\) associated with the 2\(p\)th root of unity \(q=\exp(\pi\sqrt{-1}/p)\). Then we have NEWLINE\[NEWLINE \tau_{2p}^{SU(2)}(M,\theta)\in\begin{cases} (\xi-1)\mathbb Z[1/2,\xi]&\text{if}\quad \theta\cup\theta\cup\theta=0,\\ \sqrt{-1}(\xi-1)\mathbb Z[1/2,\xi]&\text{if}\quad \theta\cup\theta\cup\theta\not =0.\end{cases} NEWLINE\]NEWLINE where \(\xi=\exp(2\pi\sqrt{-1}/p)\)''.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00034].