Intersection cohomology of character varieties for punctured Riemann surfaces

Abstract

We study intersection cohomology of character varieties for punctured Riemann surfaces with prescribed monodromies around the punctures. Relying on previous result from Mellit for semisimple monodromies we compute the intersection cohomology of character varieties with monodromies of any Jordan type. This proves the Poincar\'e polynomial specialization of a conjecture from Letellier.