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تسجيل مستخدم جديدA note on the $Theta$-invariant of 3-manifolds
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In this note, we revisit the $Theta$-invariant as defined by R. Bott and the first author. 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.
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