There is already a generalized description of classes of moduli spaces of geometric structures on surfaces by Giansiracusa. That description includes moduli of spin surfaces, $r$-spin surfaces, surfaces with a principal G-bundle, surfaces with maps to a background space, among others. Here, we want to compute the homotopy groups of the moduli spaces of $k$-Higgs bundles, with the modular operads as main tool, and then, compare them with the results of Hausel and the results of Bradlow~et.al. Joint work with Jesús E. Sánchez Guevara.