Dynamics on Lorentz manifolds / / Scot Adams

• Record Nr.: UNINA9910826713803321
• Autore: Adams Scot
• Pubbl/distr/stampa: River Edge, N.J., : World Scientific, c2001
• ISBN: 1-281-95624-4; 9786611956240; 981-281-056-0
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (416 p.)
• Disciplina: 514.3
• Soggetti: Manifolds (Mathematics); Topology
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 391-393) and index.
• Nota di contenuto: Preface; Contents; Chapter 1 Introduction History and Outline; 1.1 Lorentz manifolds and relativity; 1.2 Symmetries of Lorentz manifolds; 1.3 Outline of succeeding chapters; 1.4 Notation; 1.5 Acknowledgements; Chapter 2 Basic Results and Definitions; 2.1 Some set-theoretic notions; 2.2 Some group-theoretic notions; 2.3 Some topological notions; 2.4 Some notions from linear algebra; 2.5 Matrix concentration lemmas; 2.6 First results on expansive sequences; 2.7 Topological groups; 2.8 Discrete groups; 2.9 Proper actions; 2.10 Bilinear and quadratic forms; 2.11 Root systems; 2.12 Minkowski forms - basic definitionsChapter 3 Basic Differential Topology; 3.1 Some differential topological notions; 3.2 Inheritability of continuity and smoothness to leanike submanifolds; 3.3 Definition of prefoliation and foliation; 3.4 Preliminary results to the Frobenius Theorem; 3.5 Uniqueness in the Frobenius Theorem; 3.6 Passage from local to global in the Frobenius Theorem; 3.7 The Frobenius Theorem; 3.8 Potential submersions; 3.9 Lorentz metrics - basic definitions; Chapter 4 Basic Lie Theoretic Results; 4.1 Some Lie theoretic definitions and notation; 4.2 Dynamical consequences of the Frobenius Theorem4.3 exp Ad and ad; 4.4 The Lie group Lie algebra correspondence; 4.5 Some facts about Lie subgroups; 4.6 The Lie algebra of [AB]; 4.7 Lie groups and Lie ; algebras from bilinear and quadratic forms; 4.8 Abelian Lie groups; 4.9 Miscellaneous results; 4.10 Generalities on semisimple groups and algebras; 4.11 Real Jordan decomposition; 4.12 Consequences of results on real Jordan decomposition; 4.13 Generalities on algebraic groups; 4.14 Generalities on nilpotent groups and algebras; 4.15 Generalities on the nilradical; 4.16 Relationships between representation theoriesChapter 5 More Lie Theory; 5.1 Connection-preserving diffeomorphisms form a Lie group; 5.2 The isometry group of a pseudoRiemannian manifold is a Lie group; 5.3 More results on expansive sequences; 5.4 Lie groups densely embedded in other Lie groups; 5.5 Generalities on the Levi decomposition; 5.6 Large normalizers and centralizers; 5.7 Representation theory; Chapter 6 Minkowski Linear Algebra; 6.1 Notations for important elements and Lie subalgebras of so(Qd); 6.2 Linear algebra of Minkowski vector spaces; 6.3 Basic calculations; 6.4 Embeddings of Lorentz Lie algebrasChapter 7 Basic Dynamical Results; 7.1 Kowalsky's Lemma; 7.2 Higher jets of vector fields and metrics - notation; 7.3 Matrix realizations of jets and calculus on jets; 7.4 Miscellaneous results; 7.5 A basic collection of rigidity results; 7.6 Strongly lightlike and nontimelike vectors; 7.7 Basic results on degenerate orbits; 7.8 More on strongly lightlike and nontimelike vectors; 7.9 Nonproperness and cocompact subgroups; 7.10 Kowalsky subsets; 7.11 Types of chaotic actions; 7.12 Induction of actions: Definition; 7.13 Induction of actions: Basic results; 7.14 Riemannian dynamics
• Sommario/riassunto: Within the general framework of the dynamics of "large" groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions. This particular area of dynamics is an active one, and not all the results are in their final form. However, at this point, a great deal can be said about the particular Lie groups that come up in this context. It is impressive that, even assuming very weak recurrence of the action, the list of possible groups is quite restricted. For the most complicated of the