Expository Article: Young person's guide to translation surfaces of genus two: McMullen's connected sum theorem
Andrew Bouwman, Jarosław Kwapisz · Rocky Mountain Journal of Mathematics · 2013
A translation surface is a surface obtained by identifying pairs of parallel edges of a polygon in the Cartesian plane R 2 .We give an introduction to translation surfaces of genus two including their hyperellipticity and a detailed elementary proof of McMullen's result that any such surface can be obtained as a connected sum of two flat tori.