ABSTRACT

This chapter surveys computational topology results in the special, low-dimensional case where the ambient space is a surface. Surface topology is very well-understood and comparably simpler than the higher-dimensional counterparts; many computational problems that are undecidable in general (e.g., homotopy questions) can be solved efficiently on surfaces. This leads to a distinct flavor of computational topology and to dedicated techniques for revisiting topological problems on surfaces from a computational viewpoint.