Smooth Parametrizations for Tori With Genus Greater Than 1

Cullen, Allison, Joseph Furgal, and Abhijit Dasgupta

A torus of genus 1 is the surface of doughnut — it is an orientable closed compact 2-surface. Easy and well known smooth parametrizations exist for the genus-i torus. It is much harder to find simple smooth parametrizations for tori of higher genus. In this work, we explore such smooth parametrizations.