Motive of the $S{L}_4$-character variety of torus knots

Abstract

In this paper, we compute the motive of the character variety of representations of the fundamental group of the complement of an arbitrary torus knot into $S{L}_4(k)$, for any algebraically closed field $k$ of zero characteristic. For that purpose, we introduce a stratification of the variety in terms of the type of a canonical filtration attached to any representation. This allows us to reduce the computation of the motive to a combinatorial problem.

37 pages. Note: download source for the output of all the strata as separate file

References in corpus (4)

• Counting Gauge Invariants: the Plethystic Program
• Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups
• Virtual classes of parabolic ${\mathrm{SL}}_2(\mathbb{C})$-character varieties
• Serre polynomials of $S{L}_n$- and $PG{L}_n$-character varieties of free groups

Cited by in corpus (1)

• Representation varieties of twisted Hopf links