Manifolds of Nonpositive Curvature

ISBN-13: 9781468491616 / Angielski / Miękka / 2013 / 266 str.

Werner Ballmann;Misha Gromov;Viktor Schroeder

Opis

This volume presents a complete and self-contained description of new results in the theory of manifolds of nonpositive curvature. It is based on lectures delivered by M. Gromov at the College de France in Paris. Therefore this book may also serve as an introduction to the subject of nonpositively curved manifolds. The latest progress in this area is reflected in the article of W. Ballmann describing the structure of manifolds of higher rank.

Spis treści

Preface.-Introduction.-Lectures on Manifolds of Nonpositive Curvature.-Simply Connected Manifolds of Nonpositive Curvature.-Groups of Isometries.-Finiteness theorems.-Strong Rigidity of Locally Symmetric Spaces.-Appendix 1. Manifolds of Higher Rank.-Appendix 2: Finiteness Results for Nonanalytic Manifolds.-Appendix 3: Tits Metric and the Action of Isometries at Infinity.-Appendix 4: Tits Metric and Asymptotic Rigidity.-Appendix 5: Symmetric Spaces of Noncompact types.-References.-Subject Index.

Blurb

This volume presents a complete and self-contained description of new results in the theory of manifolds of nonpositive curvature. It is based on lectures delivered by M. Gromov at the Collège de France in Paris. Among others these lectures threat local and global rigidity problems (e.g., a generalization of the famous Mostow rigidity theorem) and finiteness results for manifolds of finite volume. V. Schroeder wrote up these lectures, including complete and detailed proofs. A lot of background material is added to the first lectures. Therefore this book may also serve as an introduction to the subject of nonpositively curved manifolds. The latest progress in this area is reflected in the article of W. Ballmann describing the structure of manifolds of higher rank.