Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
Abstract: 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.
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| Format: | Digital revista |
| Language: | English |
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Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2018
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| Online Access: | http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262018000100009 |
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