A note on the $\Theta$-invariant of 3-manifolds

Alberto S. Cattaneo; Tatsuro Shimizu

doi:10.4171/qt/146

JournalsqtVol. 12, No. 1pp. 111–127

A note on the $Θ$ -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 $Θ$ -invariant as defined by R. Bott and the first author in [4]. The $Θ$ -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 $Θ$ -invariant can be defined when a cohomology group is vanishing. In this note, we give a slightly modified version of the $Θ$ -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 $Θ$ -invariant of 3-manifolds. Quantum Topol. 12 (2021), no. 1, pp. 111–127

DOI 10.4171/QT/146