Contenu
"A natural question that sits at the nexus of algebraic geometry, differential geometry, and geometric group theory is: which groups can be realized as fundamental groups of compact Kèahler manifolds, called "Kèahler groups"? Roughly speaking, the fundamental group of a manifold measures the number of "holes." Many restrictions are known, and many examples are known; but mathematicians are far from having a precise conjecture about which groups are Kèahler. The question serves as a fruitful connection between several major areas of geometry and complex analysis. Py's book is an up-to-date pedagogical survey of the central theorems and methods for the study of Kèahler groups including, where illuminating, detailed proofs. It includes results of Gromov, Schoen, Napier, Ramachandran, Corlette, Simpson, Delzant, Arapura, and Nori. The charm of the subject is that different methods yield information of different flavors, and the challenge is to draw these threads together. This book leans toward geometric group theory, but it gives a coherent account of great value to anyone interested in Kèahler groups - and in Kèahler manifolds more broadly. The emphasis is on unity and cross-fertilization among approaches"--