Geometric Topology: Recent Developments: Lectures given on the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Monteca- ... 1504 (Lecture Notes in Mathematics, 1504) - Softcover

Cheeger, Jeff; Gromov, Mikhail; Okonek, Christian; Pansu, Pierre

 
9783540550174: Geometric Topology: Recent Developments: Lectures given on the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Monteca- ... 1504 (Lecture Notes in Mathematics, 1504)

Synopsis

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.

"synopsis" may belong to another edition of this title.

Synopsis

The text of three lectures on geometric topology are presented in this volume. There is a discussion of the geometry and rigidity of discrete subgroups in Lie groups and an examination of the theory of moduli space of instantons as a tool for studying the geometry of low-dimensional manifolds.

"About this title" may belong to another edition of this title.