2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/194346In the context of loop quantum gravity, we construct the phase-space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase-space is calculated including the genus cycles as degrees of freedom. From this, the black hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading term agrees with the A/4 law and that the sub-leading contribution is modified by the genus cycles.22 pages, 9 figures. References updated. Minor changes to match version to appear in Class. Quant. GravGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext