English

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

Geometric Topology 2021-05-14 v1

Abstract

In this note, we revisit the Θ\Theta-invariant as defined by R. Bott and the first author. The Θ\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 Θ\Theta-invariant can be defined when a cohomology group is vanishing. In this note, we give a slightly modified version of the Θ\Theta-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