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

Creative Commons License

ZEYBEK H.

GEOMETRIAE DEDICATA, cilt.213, sa.1, ss.401-421, 2021 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 213 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s10711-020-00588-6
  • Dergi Adı: GEOMETRIAE DEDICATA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.401-421
  • Anahtar Kelimeler: Shearing deformations, Hitchin representations, Atiyah-Bott-Goldman symplectic form
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.