A note on the $\Theta$-invariant of 3-manifolds
Geometric Topology
2021-05-14 v1
Abstract
In this note, we revisit the -invariant as defined by R. Bott and the first author. 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.
Keywords
Cite
@article{arxiv.1903.04386,
title = {A note on the $\Theta$-invariant of 3-manifolds},
author = {Alberto S. Cattaneo and Tatsuro Shimizu},
journal= {arXiv preprint arXiv:1903.04386},
year = {2021}
}
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13 pages