Higgs bundles, pseudo-hyperbolic geometry and maximal representations
نویسندگان
چکیده
منابع مشابه
Geometry of Moduli Spaces of Higgs Bundles
We construct a Petersson-Weil type Kähler form on the moduli spaces of Higgs bundles over a compact Kähler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature of a certain determinant line bundle, equipped with a Quillen metric, on the moduli space of Higgs bundles over a projective manifold. The curvature of the Peters...
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Today will be mostly preliminaries, including some complex and symplectic geometry, such as the symplectic quotient, and an introduction to Kähler and hyperkähler geometry. Over the rest of the week, we’ll discuss some examples (which are usually left implicit) such as quiver varieties, introduce the moduli space of Higgs bundles, and more. A good reference for this is Andy Neitzke’s lecture no...
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Introduction 1 1. Representations of the fundamental group 3 2. Abelian groups and rank one Higgs bundles 5 3. Stable vector bundles and Higgs bundles 6 4. Hyperbolic geometry: G = PSL(2,R) 8 5. Moduli of hyperbolic structures and representations 13 6. Rank two Higgs bundles 19 7. Split R-forms and Hitchin’s Teichmüller component 21 8. Hermitian symmetric spaces: Maximal representations 24 Refe...
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Preface The present dissertation is my own work, except where attributed to others. It is not the outcome of work done in collaboration, except Chapters 6 and 7. Chapters 6 and 7 describe joint work with Michael Thaddeus. We started a correspondence in early 1997 about [Tha1] and related problems. The results appearing in these chapters were mostly achieved when we participated in the Research ...
متن کاملModuli of Higgs Bundles
2 Local symplectic, complex and Kähler geometry: a quick review 10 2.1 Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Symplectic manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Symplectic quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Complex manifolds . . . . . . . . . . . . . . ....
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ژورنال
عنوان ژورنال: Séminaire de théorie spectrale et géométrie
سال: 2017
ISSN: 2118-9242
DOI: 10.5802/tsg.357