Geometric Topology: Recent Developments

Geometric Topology can be defined to be the investigation of

global properties of a further structure (e.g.

differentiable, Riemannian, complex,algebraic etc.) one can

impose on a topological manifold. At the C.I.M.E. session in

Montecatini, in 1990, three courses of lectures were given

onrecent developments in this subject which is nowadays

emerging as one of themost fascinating and promising fields

of contemporary mathematics. The notesof these courses are

collected in this volume and can be described as: 1) the

geometry and the rigidity of discrete subgroups in Lie

groups especially in the case of lattices in semi-simple

groups; 2) the study of the critical points of the distance

function and its appication to the understanding of the

topology of Riemannian manifolds; 3) the theory of moduli

space of instantons as a tool for studying the geometry of

low-dimensional manifolds.

CONTENTS: J. Cheeger: Critical Points of Distance Functions

and Applications to Geometry.- M. Gromov, P. Pansu, Rigidity

of Lattices: An Introduction.- Chr. Okonek: Instanton

Invariants and Algebraic Surfaces.