Virtual Hodge polynomials of the moduli spaces of representations of degree 2 for free monoids

Abstract

In this paper we study the topology of the moduli spaces of representations of degree $2$ for free monoids. We calculate the virtual Hodge polynomials of the character varieties for several types of $2$-dimensional representations. Furthermore, we count the number of isomorphism classes for each type of $2$-dimensional representations over any finite field ${\mathbb{F}}_q$, and show that the number coincides with the virtual Hodge polynomial evaluated at $q$.

23 pages

References in corpus (2)

• E-polynomial of the SL(3,C)-character variety of free groups
• The moduli of representations of degree 2