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" The geometry, topology, and physics of moduli spaces of Higgs bundles / "
editors, Richard Wentworth (University of Maryland, USA), Graeme Wilkin (NUS, Singapore).
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BL
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| Record Number
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890619
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| Title & Author
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The geometry, topology, and physics of moduli spaces of Higgs bundles /\ editors, Richard Wentworth (University of Maryland, USA), Graeme Wilkin (NUS, Singapore).
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| Publication Statement
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New Jersey :: World Scientific,, 2018.
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| Series Statement
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Lecture notes series / Institute for Mathematical Sciences, National University of Singapore ;; volume 36
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1 online resource
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| ISBN
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9789813229099
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: 9813229098
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9789813229082
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981322908X
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Contents; Foreword; Preface; An Introduction to the Differential Geometry of Flat Bundles and of Higgs Bundles; 1. Introduction; 2. Riemannian, symplectic, complex and Kählerian manifolds; 2.1. Riemannian manifold; 2.2. Orientation, volume form; 2.3. The Hodge star; 2.4. Symplectic manifold; 2.5. The symplectic star; 2.6. The operator L; 2.7. Symplectic adjoints; 2.8. Symplectic Kähler identities; 2.9. Complex (analytic) manifolds; 2.10. Kähler manifold; 2.11. Adjoints and stars; 2.12. Kähler identities; 3. Vector bundles; 3.1. Trivializations; 3.2. Changes of trivializations
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2. Spectral data for Gc-Higgs bundles2.1. Gc-Higgs bundles; 2.1.1. Moduli space of vector bundles; 2.1.2. Moduli space of classical Higgs bundles; 2.1.3. Moduli space of Gc-Higgs bundles; 2.2. The Hitchin fibration; 2.2.1. GL(n, C)-Higgs bundles; 2.2.2. SL(n, C)-Higgs bundles; 2.2.3. Sp(2n, C)-Higgs bundles; 2.2.4. SO(2n + 1, C)-Higgs bundles; 2.2.5. SO(2n, C)-Higgs bundles; 2.3. Spectral data for complex Higgs bundles; 3. Spectral data for G-Higgs bundles; 3.1. G-Higgs bundles; 3.1.1. Real forms; 3.1.2. G-Higgs bundles through involutions; 3.2. Spectral data for G-Higgs bundles
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3.3. From cocyles to bundles3.4. Linear algebra; 3.5. The gauge group; 3.6. Spaces of sections; 4. Flat bundles; 4.1. Flat structures; 4.2. Flat bundles and representations of the fundamental group; 4.3. From representations to flat bundles; 5. Holomorphic vector bundles; 5.1. Holomorphic bundles and their trivializations; 5.2. Pseudo-connection; 5.3. Pseudo-curvature; 5.4. The space of pseudo-connections; 5.5. The action of the gauge group; 6. Flat bundles and connections; 6.1. Connections; 6.2. Curvature; 7. Chern connections, stability, degree; 7.1. Hermitian structure
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7.2. Unitary connections over a complex manifold7.3. L2-metrics; 7.4. Another kind of adjunction; 7.5. Kähler manifold; 7.6. Chern characters; 7.7. Degree; 7.8. Stability; 8. The correspondence between flat bundles and Higgs bundles; 8.1. The theorem of Narasimhan and Seshadri; 8.2. Higgs bundles; 8.3. The Hitchin-Kobayashi correspondence; 8.4. From flat bundles to Higgs bundles; 8.5. From Higgs bundles to flat bundles; 8.6. The case of line bundles; 8.7. Line bundles: From flat to Higgs; 8.8. Line bundles: From Higgs to flat; 9. Examples; 9.1. Every Riemann surface is Kähler
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| Subject
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Geometry, Algebraic.
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Moduli theory.
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Vector bundles.
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Geometry, Algebraic.
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MATHEMATICS-- Topology.
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Moduli theory.
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Vector bundles.
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| Dewey Classification
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514/.224
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| LC Classification
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QA612.63.G46 2018
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| Added Entry
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Wentworth, Richard A.
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Wilkin, Graeme
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