Fundamental classes of 3-manifold groups representations in SL(4,R)

Abstract

We compute the fundamental class (in the extended Bloch group) for representations of fundamental groups of [Formula: see text]-manifolds to [Formula: see text] that factor over [Formula: see text], in particular for those factoring over the isomorphism [Formula: see text]. We also discuss consequences for the number of connected components of [Formula: see text]-character varieties, and we show that there are knots with arbitrarily many components of vanishing Chern–Simons invariant in their [Formula: see text]-character varieties.