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Riemannian metrics on character varieties via Hodge theory
Andy Sanders (Heidelberg)
Aula Beltrami - Mercoledì 30 Novembre 2016 h.16:00
Abstract. > The G-character variety associated to a closed surface S and a semi simple Lie group G is the space of reductive representations of the fundamental group of S into G modulo conjugation. We will show that given any open set U of the G-character variety and any smooth map to the Teichmuller space of isotopy classes of complex structures on S, there is an associated Riemannian metric on U and an orthogonal almost-complex structure. These Hermitian structures are compatible with the natural Atiyah-Bott-Goldman symplectic structure of the G-character variety, and generalize the Weil-Petersson metric on Teichmuller space. Time permitting, we will discuss some concrete examples yielding new examples of Riemannian metrics on G-character varieties.
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