Perturbative Chern-Simons invariants from non-acyclic flat connections

TL;DR

This paper introduces a higher-loop perturbative invariant for framed 3-manifolds, extending previous invariants to include non-acyclic flat connections by integrating a Chern-Simons volume form over moduli space components.

Contribution

It generalizes the perturbative Chern-Simons invariant to non-acyclic flat connections using a new integral construction over moduli space.

Findings

Defines a new invariant for non-acyclic flat connections

Extends the scope of perturbative Chern-Simons invariants

Provides a framework for higher-loop invariants in 3-manifold topology

Abstract

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.