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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
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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.
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