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

Elisha Falbel (1, 2, 3) , Qingxue Wang (4)

1 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs
2 UPMC - Université Pierre et Marie Curie - Paris 6
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
4 School of Mathematical Sciences [Shanghai]

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

Domaines: Mathématiques générales [math.GM]

Elisha Falbel, Qingxue Wang. Duality and invariants of representations of fundamental groups of 3-manifolds into PGL(3,C). Bulletin of the London Mathematical Society, 2017, 95 (Part1), pp.1-22. ⟨10.1112/jlms.12004⟩. ⟨hal-01374795⟩