本书详尽阐述了关于紧K?hler流形的基本群目前已知的方方面面。这个群类包括所有有限群，并且严格小于所有有限展示的群类。本书第一次收集了过去几年获得的所有结果，旨在描述那些可作为紧K?hler流形的基本群出现的无限群。这些结果大多数都是反例，说明哪些群不会出现。这些结果可以用Hodge理论及其与有理同伦、L2上同调、调和映射和规范理论的结合来证明。也有许多正面的结果，展示了一些有趣的K?hler流形的基本群，事实上，即光滑复射影簇的基本群。 本书所使用的方法和技术将拓扑、微分和代数几何、复分析完美地融合在一起，适合对相关领域感兴趣的研究人员和研究生阅读，也可用作高年级研究生的教科书，其突出特点之一是包含了大量的具体示例。 本书包含了许多以前未曾出现过的新的结果和例子，并讨论了该领域一些重要的未解决问题。 本书是目前唯一涉及这一主题的书籍，几何学家应该对此感兴趣……并且也适合对这些主题感兴趣的研究生阅读。 —Bulletin of the London Mathematical Society

前辅文
Chapter 1 Introduction
  1.Kahler geometry
  2.Kahler and non-Kahler groups
  3.Fundamental groups of compact complex surfaces
  4.Complex symplectic non-Kahler manifolds
Chapter 2 Fibering Kahler manifolds and Kahler groups
  1.The fibration problem
  2.The Albanese map and free Abelian representations
  3.Fibering over Riemann surfaces
  4.Fibering compact complex surfaces
Chapter 3 The de Rham fundamental group
  1.The de Rham fundamental group and the 1-minimal model
  2.Formality of compact Kahler manifolds
  3.Applications to the fundamental group and examples
  4.The Albanese map and the de Rham fundamental group
  5.Non-fibered Kahler groups
  6.Mixed Hodge structures on the de Rham fundamental group
Chapter 4 L2-cohomology of Kahler groups
  1.Introduction
  2.Simplicial L2-cohomology and ends
  3.de Rham L2-cohomology
  4.Fibering Kahler manifolds over D2
  5.Fibering Kahler manifolds over Riemann surfaces
Chapter 5 Existence theorems for harmonic maps
  1.Definitions
  2.Hartman's uniqueness theorem
  3.The Eells-Sampson theorem
  4.Equivariant harmonic maps
Chapter 6. Applications of harmonic maps
  1.Existence of pluriharmonic maps
  2.First applications
  3.Period domains
  4.The factorisation theorem
  5.Non-linear groups
  6.Harmonic maps to trees
Chapter 7 Non-Abelian Hodge theory
  1.Basic concepts
  2.Yang-Mills equations and the C*-action on Higgs bundles
  3.Hyperkahler structures and complete integrability
  4.Applications
Chapter 8 Positive results for infinite groups
  1.Introduction
  2.The first construction
  3.A Lefschetz theorem for smooth open varieties
  4.The general construction
  5.Non-residually finite Kahler groups
Appendix A. Pro group theory
  1.Definitions of group completions
  2.Nilpotent completions
  3.Comparison of nilpotent completions
Appendix B. A glossary of Hodge theory
Bibliography
Index