A note on exceptional groups and Reidemeister torsion


Hezenci F., SÖZEN Y.

JOURNAL OF MATHEMATICAL PHYSICS, vol.59, no.8, 2018 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 8
  • Publication Date: 2018
  • Doi Number: 10.1063/1.5021318
  • Journal Name: JOURNAL OF MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded, Scopus

Abstract

Let Sigma be a closed orientable surface of genus at least 2 and G be one of the exceptional groups G(2), F-4, and E-6. The present article considers the set Rep(Sigma, G) of G-valued representations from the fundamental group pi(1)(Sigma) of the surface Sigma 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(Sigma, G), namely, the Atiyah-Bott-Goldman symplectic form for the Lie group G. Moreover, it applies to G-valued Hitchin representations. Published by AIP Publishing.