A note on exceptional groups and Reidemeister torsion

Abstract

Let Σ be a closed orientable surface of genus at least 2 and G be one of the exceptional groups G2, F4, and E6. The present article considers the set Rep(Σ, G) of G-valued representations from the fundamental group π1(Σ) of the surface Σ to the exceptional group G. It proves that for such representations the notion of Reidemeister torsion is well-defined. It also establishes a formula for computing Reidemeister torsion of such representations in terms of the well-known symplectic structure on Rep(Σ, G), namely, the Atiyah-Bott-Goldman symplectic form for the Lie group G. Moreover, it applies to G-valued Hitchin representations.