Geometric Topology: Recent Developments
Lectures given on the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Monteca- tini Terme, Italy, June 4-12, 1990
Samenvatting
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.