Arithmetic of character varieties of free groups
  Via counting over finite fields, we derive explicit formulas for the E-polynomials and Euler characteristics of GL(d)- and PGL(d)-character varieties of free groups. We prove a positivity property for these polynomials and relate them to the number of subgroups of finite index. 
Sergey Mozgovoy, Markus Reineke
math.AG math.GR math.RT