Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Kähler groups and rigidity phenomena

F. E. A. Johnsona1 and E. G. Reesa2

a1 Department of Mathematics, University College London, Gower Street, London WC1E 6BT

a2 Department of Mathematics, University of Edinburgh, The King's Buildings, Edinburgh EH9 3JZ

The class S0305004100069541_xs1D4AB of fundamental groups of non-singular complex projective varieties is an interesting, but as yet imperfectly understood, class of finitely presented groups. Membership of S0305004100069541_xs1D4AB is known to be extremely restricted (see [22, 23]). In this paper, we employ geometrical rigidity properties to realize some group extensions as elements of S0305004100069541_xs1D4AB as in our previous papers, we find it convenient to work simultaneously with the class xs210B of fundamental groups of compact Kähler manifolds.

(Received July 10 1989)

(Revised May 02 1990)