Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
| Autor: | Ronald A. Zúñiga-Rojas |
|---|---|
| Jazyk: | Spanish; Castilian |
| Rok vydání: | 2018 |
| Předmět: |
Homotopy group
Pure mathematics General Mathematics Moduli of Higgs Bundles 010102 general mathematics Vector bundle 01 natural sciences 55Q52 14H60 14D07 Stratification (mathematics) Moduli space Variaciones de Estructuras de Hodge Mathematics::Algebraic Geometry Vector Bundles Fibrados Vectoriales 51 Matemáticas / Mathematics Higgs boson FOS: Mathematics Algebraic Topology (math.AT) Moduli de Fibrados de Higgs Compact Riemann surface Mathematics - Algebraic Topology Variations of Hodge Structures 0101 mathematics Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Repositorio UN Universidad Nacional de Colombia instacron:Universidad Nacional de Colombia |
| Popis: | The work of Hausel proves that the Bia\l{}ynicki-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 space 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 $\mathcal{M}^k(2,d)$, and generalize it to $\mathcal{M}^k(3,d)$, the moduli spaces of $k$-Higgs bundles of degree $d$, and ranks two and three respectively, using the results from the works of Hausel and Thaddeus, among other tools. Comment: 19 pages, v3 updated version, corrected typos; to appear in Revista Colombiana de Matem\'aticas |
| Databáze: | OpenAIRE |
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