Intersection cohomology of rank two character varieties of surface groups
Abstract
For G = GL2, SL2, PGL2 we compute the intersection E-polynomials and the intersection Poincar\'e polynomials of the G-character variety of a compact Riemann surface C and of the moduli space of G-Higgs bundles on C of degree zero. We derive several results concerning the P=W conjectures for these singular moduli spaces.
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