The EMS Publishing House is now **EMS Press** and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

# Quantum Topology

Full-Text PDF (159 KB) | Metadata | Table of Contents | QT summary

**Volume 12, Issue 1, 2021, pp. 111–127**

**DOI: 10.4171/QT/146**

Published online: 2021-03-15

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

Alberto S. Cattaneo^{[1]}and Tatsuro Shimizu

^{[2]}(1) Universität Zürich, Switzerland

(2) Kyoto University, Japan

In this note, we revisit the $\Theta$-invariant as defined by R. Bott and the first author in [4]. The $\Theta$-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 $\Theta$-invariant can be defined when a cohomology group is vanishing. In this note, we give a slightly modified version of the $\Theta$-invariant that we can define even if the cohomology group is not vanishing.

*Keywords: *Invariants of 3-manifolds, Chern–Simons perturbation theory, configuration space integral

Cattaneo Alberto, Shimizu Tatsuro: A note on the $\Theta$-invariant of 3-manifolds. *Quantum Topol.* 12 (2021), 111-127. doi: 10.4171/QT/146