The Chern-Simons invariants for the double of a compression body

TL;DR

This paper computes Chern-Simons invariants for doubles of compression bodies and shows the connectedness of the moduli space of flat connections under certain conditions.

Contribution

It provides explicit calculations of Chern-Simons critical values for these 3-manifolds and establishes the connectedness of the moduli space of flat connections without reducibles.

Findings

Computed Chern-Simons critical values for arbitrary compact groups.

Proved the moduli space of flat connections is connected when reducibles are absent.

Extended understanding of invariants for a class of 3-manifolds.

Abstract

Given a 3-manifold that can be written as the double of a compression body, we compute the Chern-Simons critical values for arbitrary compact connected structure groups. We also show that the moduli space of flat connections is connected when there are no reducibles.