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The physics of topological insulators makes it possible to understand andpredict the existence of unidirectional waves trapped along an edge or aninterface. In this review, we describe how these ideas can be adapted togeophysical and astrophysical waves. We deal in particular with the case ofplanetary equatorial waves, which highlights the key interplay between rotationand sphericity of the planet, to explain the emergence of waves which propagatetheir energy only towards the East. These minimal ingredients are preciselythose put forward in the geometric interpretation of the Foucault pendulum. Wediscuss this classic example of mechanics to introduce the concepts of holonomyand vector bundle which we then use to calculate the topological properties ofequatorial shallow water waves.

From the geometry of Foucault pendulum to the topology of planetary waves