A note on the -invariant of 3-manifolds

  • Alberto S. Cattaneo

    Universität Zürich, Switzerland
  • Tatsuro Shimizu

    Kyoto University, Japan
A note on the $\Theta$-invariant of 3-manifolds cover
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Abstract

In this note, we revisit the -invariant as defined by R. Bott and the first author in [4]. The -invariant is an invariant of rational homology 3-spheres with acyclic orthogonal local systems, which is a generalization of the 2-loop term of the Chern–Simons perturbation theory. The -invariant can be defined when a cohomology group is vanishing. In this note, we give a slightly modified version of the -invariant that we can define even if the cohomology group is not vanishing.

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Alberto S. Cattaneo, Tatsuro Shimizu, A note on the -invariant of 3-manifolds. Quantum Topol. 12 (2021), no. 1, pp. 111–127

DOI 10.4171/QT/146