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

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ZEYBEK H.

GEOMETRIAE DEDICATA, vol.213, no.1, pp.401-421, 2021 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 213 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1007/s10711-020-00588-6
  • Journal Name: GEOMETRIAE DEDICATA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.401-421
  • Keywords: Shearing deformations, Hitchin representations, Atiyah-Bott-Goldman symplectic form
  • Open Archive Collection: AVESIS Open Access Collection
  • Hacettepe University Affiliated: Yes

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.