Chern Numbers and Rozansky-Witten Invariants of Compact Hyper-Kähler Manifolds - Info and Reading Options

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Intro -- Chern Numbers and Rozansky-Witten Invariants of Compact Hyper-Kahler Manifolds -- Contents -- Preface -- Introduction -- Notation -- 1. Compact hyper-Kahler manifolds and holomorphic symplectic manifolds -- 1.1 Basics on compact hyper-Kahler manifolds -- 1.1.1 Holonomy of Riemannian manifolds -- 1.1.2 Definition of a compact hyper-Kahler manifold -- 1.1.3 Holomorphic symplectic manifolds -- 1.1.4 Deformations of compact complex manifolds -- 1.2 Examples -- 1.2.1 The K3 surface -- 1.2.2 The Hilbert scheme of points on a surface -- 1.2.3 Construction of line bundles and classes in H2 on the Hilbert schemes of points on surfaces -- 1.2.4 Hilbert schemes of points on K3 surfaces -- 1.2.5 Generalised Kummer varieties -- 1.2.6 Further examples -- 1.3 Characteristic classes -- 1.3.1 Symplectic sheaves -- 1.3.2 Characteristic classes of symplectic sheaves -- 1.3.3 Chern numbers of holomorphic symplectic manifolds -- 1.4 The Atiyah class -- 1.4.1 Definition -- 1.4.2 Description in terms of Cech cohomology -- 1.4.3 The Bianchi identity -- 1.4.4 Torsion and the Atiyah class of the tangent bundle -- 1.4.5 The Atiyah class of symplectic sheaves -- 1.4.6 Chern-Weil theory -- 1.5 On the second cohomology group of a hyper-Kahler manifold -- 1.5.1 The period map -- 1.5.2 A vanishing result for polynomials on H2 -- 2. Graph homology -- 2.1 The space of graph homology -- 2.1.1 Jacobi diagrams -- 2.1.2 Chains of Jacobi diagrams -- 2.1.3 Glueing legs and product of Jacobi diagrams -- 2.1.4 Subspaces and ideals -- 2.1.5 The graph homology spaces -- 2.2 Symmetric monoidal categories -- 2.2.1 Definition -- 2.2.2 k-linear categories -- 2.2.3 Global sections -- 2.2.4 External tensor and symmetric algebras -- 2.3 Metric Lie algebra objects -- 2.3.1 Definition -- 2.3.2 Examples from the category of vector spaces

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