ESP Biography

A classic math joke goes as follows:"A topologist is someone who can't tell a donut from a coffee mug." Ever wonder what that means? How can a rigid coffee mug be mistaken for a tasty donut? In this class we will explore the natural concept of a 'homotopy': deforming one object into another. Using this concept, one can say that two objects are 'similar' when the first object can be deformed into the second. For example, you might consider all pants to be similar because they all have a similar shape: two openings for feet and a bigger opening for the waist. However, homotopy goes even further: pipes of any length are considered 'similar' because they all have exactly two openings (one at each end), and can be stretched or shrunk to resemble each other. Essentially, homotopy completely forgets about lengths and distances, and only cares about the 'intrinsic' qualities of the object. You'll be using playdough to perform these deforming operations, so get ready to get your hands dirty! I will keep mathematical formalism to a minimum, and only give 'hand-waving' proofs of important results. All you really need is imagination and willingness to stretch your mind!

We will go through a basic introduction to topological spaces, and take a look at some weird, hence interesting, spaces, e.g. the Klien bottle, the Long Line, Alexander Horned Sphere etc. These counter-intuitive examples of spaces are not only fun to analyse, but also deepens our understanding of topology, making us reevaluate assumptions that we may take to be obvious.