Fundamental groups of compact Kahler manifolds / J. Amoros, ... [et al.]Type de document : MonographieCollection : Mathematical surveys and monographs, 44Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 1996Description : 1 vol. (XI-140 p.) ; 26 cmISBN : 9780821804988.ISSN : 0885-4653.Bibliographie : Bibliogr. p. 133-137. Index, glossaire.Sujet MSC : 32Q15, Complex manifolds, Kähler manifolds
58E20, Variational problems in infinite-dimensional spaces, Harmonic maps, etc.
32J27, Compact analytic spaces, Compact Kähler manifolds: generalizations, classification
53C55, Global differential geometry, Global differential geometry of Hermitian and Kählerian manifolds
14F35, (Co)homology theory in algebraic geometry, Homotopy theory and fundamental groupsEn-ligne : Zentralblatt | MathScinet | AMS
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Bibliogr. p. 133-137. Index, glossaire
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 L2 -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. (source : AMS)