Abstract
We investigate the bulk hydrodynamics of the chiral vortex matter on an arbitrary closed surface, extending the ideas of Khalatnikov (1989 Advanced Book Classics (Redwood City, CA: Addison-Wesley); Wiegmann and Abanov (2014 Phys. Rev. Lett. 113 034501). Placing this important example of a chiral medium onto a curved geometry reveals the geometric nature of odd viscosity. The anomalous odd viscosity of the vortex matter is associated with a special interaction of point vortices with curvature.
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