Fenchel-Nielsen coordinates for $$\textrm{SL}(3,{\mathbb C})$$ representations

Abstract We define Fenchel-Nielsen coordinates for representations of surface groups to $$\textrm{SL}(3,{\mathbb C})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>SL</mml:mtext> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . We also show how these coordinates relate to the classical Fenchel-Nielsen coordinates and to their generalisations by Kourouniotis, Tan, Goldman, Zhang and Parker-Platis.