Topological Acoustics

Abstract

Introduction The field of topology studies the properties of geometric objects that are preserved under continuous deformations, for example, without cutting or gluing. A cup with a handle is topologically equivalent to a donut (or a bagel if you live in New York) because one shape can be deformed into the other while preserving their common invariant hole. Exotic topological shapes, such as vortices, knots, and mobius strips, can be globally analyzed using the mathematical tools offered by topology. The connection between topology and acoustics may appear far-fetched, yet recent developments in the field of condensed matter physics and quantum mechanics have been inspiring exciting opportunities to manipulate sound in new and unexpected ways based on topological concepts.