On SL(3,$\mathbb{C}$)-representations of the Whitehead link group

Abstract

We describe a family of representations in SL(3,$\mathbb{C}$) of the fundamental group $\pi$ of the Whitehead link complement. These representations are obtained by considering pairs of regular order three elements in SL(3,$\mathbb{C}$) and can be seen as factorising through a quotient of $\pi$ defined by a certain exceptional Dehn surgery on the Whitehead link. Our main result is that these representations form an algebraic component of the SL(3,$\mathbb{C}$)-character variety of $\pi$.

20 pages, 3 figures, 4 tables, and a companion Sage notebook (see the references) v2: A few corrections and improvements

References in corpus (4)

• Geometry of the SL(3,C)-character variety of torus knots
• A 1-parameter family of spherical CR uniformizations of the figure eight knot complement
• Deformation of hyperbolic manifolds in $\mathrm{PGL}(n,\mathbf{C})$ and discreteness of the peripheral representations
• The SL(3,C)-character variety of the figure eight knot