Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles
The work of Hausel proves that the Bialynicki-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 no...
- Autores:
-
Zúñiga-Rojas, Ronald A.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2018
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66421
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66421
http://bdigital.unal.edu.co/67449/
- Palabra clave:
- 51 Matemáticas / Mathematics
Moduli of Higgs Bundles
Variations of Hodge Structures
Vector Bundles
Moduli de Fibrados de Higgs
Variaciones de Estructuras de Hodge
Fibrados Vectoriales
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | The work of Hausel proves that the Bialynicki-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 Mk(2, d), and generalize it to Mk(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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