Sur le groupe fondamental d’une variété kählérienne. (On the fundamental group of a Kähler manifold). (French) Zbl 0661.53049

We show that the cohomology \(H^ 1L_ 2\) of the fundamental group \(\Gamma\) of a compact Kähler manifold V is induced by a morphism to a Riemann surface. It follows (generalizing [F. E. A. Johnson and E. G. Rees, Bull. Lond. Math. Soc. 19, 463-466 (1987; Zbl 0608.53061)]) that \(\Gamma\) does not decompose into a non-trivial free product. Besides, if \(\Gamma\) is hyperbolic and V is aspherical, then \(H^ iL_ 2(\Gamma)=0\quad for\quad i\neq \dim_{{\mathbb{C}}}V.\)


53C55 Global differential geometry of Hermitian and Kählerian manifolds
57M05 Fundamental group, presentations, free differential calculus