Shearing deformations of Hitchin representations and the Atiyah-Bott-Goldman symplectic form


ZEYBEK H.

GEOMETRIAE DEDICATA, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2021
  • Doi Number: 10.1007/s10711-020-00588-6
  • Journal Name: GEOMETRIAE DEDICATA
  • Journal Indexes: Science Citation Index Expanded, Scopus, MathSciNet, zbMATH

Abstract

The Hitchin component Hit(n)(S) of a closed surface S is a preferred component of the character variety X-PSLn (R)(S) consisting of homomorphisms from the fundamental group pi(1)(S) to the Lie group PSLn( R), whose elements enjoy remarkable geometric and dynamical properties. We consider a certain type of deformations of the elements of Hit(n)(S), called shearing deformations, and compute their pairing for the Atiyah-Bott-Goldman symplectic form of the character variety.