Shearing deformations of Hitchin representations and the Atiyah-Bott-Goldman symplectic form
Abstract
The Hitchin component Hitn(S) of a closed surface S is a preferred component of the character variety XPSLn(R)(S) consisting of homomorphisms from the fundamental group pi1(S) to the Lie group PSLn(R)(S), whose elements enjoy remarkable geometric and dynamical properties. We consider a certain type of deformations of the elements of Hitn(S), called shearing deformations, and compute their pairing for the Atiyah-Bott-Goldman symplectic form of the character variety.
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