Perturbative Chern–Simons invariants from non-acyclic flat connections

Source abstract

In this paper, we give a short review of our construction of a higher-loop perturbative invariant of framed 3-manifolds, generalizing the perturbative Chern–Simons invariant of Witten–Axelrod–Singer, associated to an acyclic flat connection, to an invariant given by the integral of a certain “Chern–Simons volume form” over a smooth closed component of the moduli space of flat connections.