**Mathematical Surveys and Monographs**

Volume: 44;
1996;
140 pp;
Softcover

MSC: Primary 14; 32; 53;

Print ISBN: 978-0-8218-0498-8

Product Code: SURV/44

List Price: $50.00

Individual Member Price: $40.00

**Electronic ISBN: 978-1-4704-1275-3
Product Code: SURV/44.E**

List Price: $50.00

Individual Member Price: $40.00

# Fundamental Groups of Compact Kähler Manifolds

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*J. Amorós; M. Burger; K. Corlette; D. Kotschick; D. Toledo*

This book is an exposition of what is currently known about the
fundamental groups of compact Kähler manifolds.

This class of groups contains all finite groups and is
strictly smaller than the class of all finitely presentable groups. For
the first time ever, this book collects together all the results
obtained in the last few years which aim to characterise those infinite
groups which can arise as fundamental groups of compact
Kähler manifolds. Most of these results are negative ones, saying
which groups do not arise. They are proved using Hodge
theory and its combinations with rational homotopy theory,
with \(L^2\) –cohomology, with the theory of harmonic maps,
and with gauge theory. There are a number of positive results as
well, exhibiting interesting groups as fundamental groups of
Kähler manifolds, in fact, of smooth complex projective
varieties.

The methods and techniques used form an attractive mix of
topology, differential and algebraic geometry, and complex analysis. The
book would be useful to researchers and graduate students interested in
any of these areas, and it could be used as a textbook for an
advanced graduate course. One of its outstanding features is a large
number of concrete examples.

The book contains a number of new results and examples which have not
appeared elsewhere, as well as discussions of some important
open questions in the field.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry and several complex variables and analytic spaces.

#### Reviews & Endorsements

This book, presently the only one dealing with this subject, should be of interest to geometers … and be accessible to graduate students interested in these topics as well.

-- Bulletin of the London Mathematical Society

#### Table of Contents

# Table of Contents

## Fundamental Groups of Compact Kahler Manifolds

- Contents vii8 free
- Preface ix10 free
- Chapter 1. Introduction 114 free
- Chapter 2. Fibering Kähler manifolds and Kähler groups 2134
- Chapter 3. The de Rham fundamental group 2942
- 1. The de Rham fundamental group and the 1–minimal model 2942
- 2. Formality of compact Kähler manifolds 3245
- 3. Applications to the fundamental group and examples 3447
- 4. The Albanese map and the de Rham fundamental group 4053
- 5. Non–fibered Kähler groups 4356
- 6. Mixed Hodge structures on the de Rham fundamental group 4558

- Chapter 4. L[sup(2)]–cohomology of Kähler groups 4760
- Chapter 5. Existence theorems for harmonic maps 6578
- Chapter 6. Applications of harmonic maps 7184
- Chapter 7. Non–Abelian Hodge theory 91104
- Chapter 8. Positive results for infinite groups 109122
- Appendix A. Pro group theory 121134
- Appendix B. A glossary of Hodge theory 129142
- Bibliography 133146
- Index 139152