Intersection cohomology of rank two character varieties of surface groups

Abstract

For $G={\mathrm{GL}}_2,{\mathrm{SL}}_2,{\mathrm{PGL}}_2$ we compute the intersection E-polynomials and the intersection Poincaré 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.

44 pages. Comments are welcome!

References in corpus (5)

• Lectures on Nakajima's Quiver Varieties
• An overview of Morihiko Saito's theory of mixed Hodge modules
• On the E-polynomials of a family of Character Varieties
• Cell decompositions of character varieties
• On the P=W conjecture for ${\mathrm{SL}}_n$