AWM-MAA Etta Falconer Lecture 2019
Lecturer: Tara Holm, Cornell University
Topology is often called “rubber sheet geometry” and is described as “floppy” while geometry is more “rigid”. Symplectic geometry, the natural geometry of classical mechanics, is floppier than Riemannian geometry but more rigid than topology. I will give a friendly introduction to some geometric and algebraic techniques in topology, proving along the way that a topologist can turn her trousers inside out without taking them off. I will then give an overview of the floppy/rigid spectrum, motivated by many pictures and examples. I will conclude with a description how covering spaces have been useful in my own work in symplectic geometry, and how they can make square dancing more challenging.