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

Kurzfassung/Abstract

We compute the fundamental class (in the extended Bloch group) for representations of fundamental groups of 3-manifolds to SL(4,R) that factor over SL(2,C), in particular for those factoring over the isomorphism PSL(2,C)=SO(3,1). We also discuss consequences for the number of connected components of SL(4,R)-character varieties, and we show that there are knots with arbitrarily many components of vanishing Chern–Simons invariant in their SL(n,C)-character varieties.