In many cases, the near-horizon geometry encodes sufficient information to
compute conserved charges of a gravitational solution, including thermodynamic
quantities. These charges are Noether charges associated to asymptotic
isometries that preserve appropriate boundary conditions at the future horizon.
For isolated, compact horizons these charges turn out to be integrable,
conserved and finite, and they have been studied in many examples of interest,
notably in 3+1 dimensions. In higher dimensions, where the variety of horizon
structures is more diverse, it is still possible to apply the same method,
although explicit examples have so far been limited to simple topologies. In
this paper, we demonstrate that such computations can also be applied to
higher-dimensional solutions with event horizons whose spacelike cross sections
exhibit non-trivial topology. We provide several explicit examples, with
particular focus on the 5-dimensional black ring.Comment: 16 page