Duality and invariants of representations of fundamental groups of 3-manifolds into PGL(3,C)

Abstract

We determine the explicit transformation under duality of generic configurations of four flags in $\PGL(3,\bC)$ in cross-ratio coordinates. As an application we prove invariance under duality of an invariant in the Bloch group obtained from decorated triangulations of 3-manifolds.

Revised version, 29 pages,4 figures

Cited by in corpus (2)

• The bounded Borel class and complex representations of 3-manifold groups
• $\mathrm{SL}(3,\mathbb{C})$-character varieties of two-generator groups