Olivetti Club

Olu OlorodeCornell University
Jet-setting Around The World of Differential Topology

Tuesday, April 30, 2024 - 4:35pm
Malott 406

Let $X$ and $Y$ be smooth manifolds and consider the space of smooth functions from $X$ to $Y$, which we denote by $C^{\infty}(X, Y)$. In this talk I will justify why I called $C^{\infty}(X, Y)$ a space, by defining the $C^{\infty}$ (Whitney) topology, which we obtain from the topology of a fiber bundle over $X \times Y$ called the jet bundle. The elements of the jet bundle are called jets, and we will use them to "fly" to different corners of the world of differential topology. This talk will have a "choose your own adventure" style. We can explore the mapping class group, questions in 3- and 4-manifolds, Morse functions, and much more! For this talk I will not assume anything beyond some of the basics of smooth manifolds.