Contents
Preface ix
Chapter 1. Introduction 1
1. Kahler geometry 1
2. Kahler and non-Kahler groups 5
3. Fundamental groups of compact complex surfaces 10
4. Complex symplectic non-Kahler manifolds 15
Chapter 2. Fibering Kahler manifolds and Kahler groups 21
1. The fibration problem 21
2. The Albanese map and free Abelian representations 22
3. Fibering over Riemann surfaces 24
4. Fibering compact complex surfaces 27
Chapter 3. The de Rham fundamental group 29
1. The de Rham fundamental group and the 1-minimal model 29
2. Formality of compact Kahler manifolds 32
3. Applications to the fundamental group and examples 34
4. The Albanese map and the de Rham fundamental group 40
5. Non-fibered Kahler groups 43
6. Mixed Hodge structures on the de Rham fundamental group 45
Chapter 4. L2-cohomology of Kahler groups 47
1. Introduction 47
2. Simplicial
L2-cohomology
and ends 48
3. de Rham
L2-cohomology
51
4. Fibering Kahler manifolds over
D2
53
5. Fibering Kahler manifolds over Riemann surfaces 60
Chapter 5. Existence theorems for harmonic maps 65
1. Definitions 65
2. Hartman's uniqueness theorem 66
3. The Eells-Sampson theorem 66
4. Equivariant harmonic maps 67
Chapter 6. Applications of harmonic maps 71
1. Existence of pluriharmonic maps 71
2. First applications 76
3. Period domains 81
4. The factorisation theorem 82
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