Not all ravens are writing desks: An introduction to the topology of surfaces

Abstract

In the tale Alice in Wonderland, Lewis Carroll asks "Why is a raven like a writing desk?" With this open question in mind, we provide a short pedagogical introduction to the topology of surfaces, touching on the notions of orientability, open and closed surfaces, and curvature. Most of our attention will be paid to the concept of genus, which is loosely described by the number of holes a closed surface has. Following some illustrative examples, we shall apply the theory to the question at hand, conclusively stating conditions under which a writing desk is topologically equivalent to a raven. Given time, we shall relate these ideas to current research into fluid dynamics, space-times, and string theory.