E-polynomial of the SL(3,C)-character variety of free groups

Abstract

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3, C). Expanding upon existing techniques, we stratify the space of representations and compute the E-polynomial of each geometrically described stratum using fibrations. Consequently, we also determine the E-polynomial of its smooth, singular, and abelian loci and the corresponding Euler characteristic in each case. Along the way, we give new proofs of the SL(2,C), PGL(2,C), and PGL(3,C) cases.

21 pages; accepted for publication at the Pacific Journal of Mathematics

References in corpus (3)

• The topology of moduli spaces of free group representations
• Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups
• E-polynomial of SL(2,C)-Character Varieties of Free groups

Cited by in corpus (13)

• Arithmetic of singular character varieties and their $E$-polynomials
• Hodge-Deligne polynomials of character varieties of abelian groups
• Serre polynomials of $S{L}_n$- and $PG{L}_n$-character varieties of free groups
• The moduli of representations of degree 2
• Motive of the $S{L}_4$-character variety of torus knots
• Representation varieties of twisted Hopf links
• Generating series for the $E$-polynomials of $GL(n,\mathbb{C})$-character varieties
• The SL(3,C)-character variety of the figure eight knot
• Pseudo-quotients of algebraic actions and their application to character varieties
• Hodge-Deligne Polynomials of Symmetric Products of Algebraic Groups
• $e$-polynomials of character varieties
• Virtual Hodge polynomials of the moduli spaces of representations of degree 2 for free monoids
• The point counting problem in representation varieties of torus knots