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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Fundamental Groups of Compact Kahler Manifolds (Paperback)
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Fundamental Groups of Compact Kahler Manifolds (Paperback)
Series: Mathematical Surveys and Monographs
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This book is an exposition of what is currently known about the
fundamental groups of compact Kahler 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 Kahler 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 Kahler 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.
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