A course on surgery theory / / Stanley Chang, Shmuel Weinberger [[electronic resource]]

• Autore: Chang Stanley
• Pubblicazione: Princeton : , : Princeton University Press, , 2021
• Descrizione fisica: 1 online resource (472 p.) : 14 b/w illus
• Disciplina: 605
• Soggetto topico: Surgery (Topology)
• Soggetto non controllato: Borel conjecture; Chapman-Ferry; Farrell-Hsiang; Kirby-Siebenmann; L-theory; Novikov conjecture; PL category; PL topology; algebraic topology; assembly map; assembly perspective on surgery; bounded topology; classification of manifolds; controlled topology; differential topology; fibration; flat manifolds; homology manifolds; homology surgery; homotopy invariant; homotopy theory; index theorem; induction theory; manifold theory; quadratic form theory; quadratic form; representation theory; smooth category; splitting theorems; stratified spaces; surgery exact sequence; surgery obstruction group; tangent bundle; topological category; topological surgery theory; topology
• Classificazione: 415.7
• Persona (resp. second.): WeinbergerShmuel
• Note generali: Also issued in print: 2021.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Frontmatter -- Contents -- List of Figures -- Preface -- Introduction -- 1 The characterization of homotopy types -- 2 Some calculations of L-groups -- 3 Classical surgery theory -- 4 Topological surgery and surgery spaces -- 5 Applications of the assembly map -- 6 Beyond characteristic classes -- 7 Flat and almost flat manifolds -- 8 Other surgery theories -- Appendix A: Some background in algebraic topology -- Appendix B: Geometric preliminaries -- List of Symbols -- Bibliography -- Index
• Sommario/riassunto: Surgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. This book offers a modern look at this important mathematical discipline and some of its applications. In this book, Stanley Chang and Shmuel Weinberger explain some of the triumphs of surgery theory during the past three decades, from both an algebraic and geometric point of view. They also provide an extensive treatment of basic ideas, main theorems, active applications, and recent literature. The authors methodically cover all aspects of surgery theory, connecting it to other relevant areas of mathematics, including geometry, homotopy theory, analysis, and algebra. Later chapters are self-contained, so readers can study them directly based on topic interest.
• Titolo autorizzato: A course on surgery theory
• ISBN: 0-691-20035-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910554281203321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; number 211.; Princeton scholarship online.