Student colloquium

Tyrone Ghaswala, Department of Pure Mathematics University of Waterloo

“Getting a handle on surfaces”

The 2-sphere, a torus, a projective plane and a Klein bottle are examples of closed surfaces (or 2-manifolds) that are all distinct in the sense that none of the four admit homeomorphisms to any of the others. This begs the question: which distinct surfaces are able to exist and can we classify them? In exploring this question we will construct new surfaces (using handles, cross-caps and direct sums), talk about the Euler characteristic and orientability, and if we’re especially lucky, we might even spot some group theory! Time permitting we will talk briefly about the same problem for 3 and 4-manifolds, and I may even tell a joke.