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Artificial structures have been widely used to manipulate sound fields. Mostproperties of these structures derive from the material and geometry. Few areexplicitly related to the structural topology in the real space. Here, wediscover a fundamental connection between the real-space topology of acousticstructures and the topological properties of sound fields. We find that thegenus of acoustic cavities can protect the birth of singularities in velocitypolarization and isopressure line fields. The total topological index of thesurface singularities is equal to the cavities' Euler characteristic. Thisintriguing relationship is rooted in the Poincare-Hopf theorem and isirrelevant to the specific material, geometric details, or excitationproperties. The isopressure line singularities lead to acoustic hotspots andquiet zones. The velocity polarization singularities give rise to nontrivialpolarization Mobius strips and skyrmion textures. The results enable soundsculpturing with structural topology and can find applications in acousticcommunications, acoustic sensing, and noise control.

Sculpturing sound fields with real-space topology