Dynamics on Lorentz Manifolds

Résumé du livre

Within the general framework of the dynamics of OC largeOCO 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 these groups, one can also describe reasonably well the local structure of the actions that arise. This advanced text is also appropriate to a course for mathematics graduate students who have completed their first year of study. Contents: Introduction, History and Outline; Basic Results and Definitions; Basic Differential Topology; Basic Lie Theoretic Results; More Lie Theory; Minkowski Linear Algebra; Basic Dynamical Results; Examples of Actions on Compact Lorentz Manifolds; Examples of Nonproper Actions; Semisimple Groups Admitting a Nonproper Action; Groups with Action on a Compact Lorentz Manifold; The Isometry Group of a Compact Lorentz Manifold; Highly Symmetric Compact Lorentz Manifolds; Locally Free Orbit Nonproper Lorentz Actions; Orbit Nonproper Lorentz Actions; Appendices: The Borel Density Theorem; Tameness of Algebraic Actions in Characteristic Zero. Readership: Researchers and graduate students in mathematics, mathematical physics and theoretical physics."