Abstract

ZUNIGA-ROJAS, Ronald A.. Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles. Rev.colomb.mat. [online]. 2018, vol.52, n.1, pp.9-31. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v1n52.74525.

The work of Hausel proves that the Białynicki-Birula stratification of the moduli space of rank two Higgs bundles coincides with its Shatz stratification. He uses that to estimate some homotopy groups of the moduli spaces of k-Higgs bundles of rank two. Unfortunately, those two stratifications do not coincide in general. Here, the objective is to present a different proof of the stabilization of the homotopy groups of M k (2, d), and generalize it to M k (3, d), the moduli spaces of k-Higgs bundles of degree d, and ranks two and three respectively, over a compact Riemann surface X, using the results from the works of Hausel and Thaddeus, among other tools.

Keywords : Moduli of Higgs Bundles; Variations of Hodge Structures; Vector Bundles.

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