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Global Riemannian Geometry: Curvature and Topology
This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.
Shape, Smoothness, and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback
This book contains recent results about the global dynamics defined by a class of delay differential equations which model basic feedback mechanisms and arise in a variety of applications such as neural networks. The authors describe in detail the geometric structure of a fundamental invariant set, which in special cases is the global attractor, and the asymptotic behavior of solution curves on it. The approach makes use of advanced tools which in recent years have been developed for the investigation of infinite-dimensional dynamical systems: local invariant manifolds and inclination lemmas for noninvertible maps, Floquet theory for delay differential equations, a priori estimates controlli...
Perspectives in Riemannian Geometry
Special geometries as well as the relation between curvature and topology have always been of interest to differential geometers. More recently, these topics have turned out to be of use in physical problems related to string theory as well. This volume provides a unique and thorough survey on the latest developments on Riemannian geometry, special geometrical structures on manifolds, and their interactions with other fields such as mathematical physics, complex analysis, andalgebraic geometry. This volume presents ten papers written by participants of the ``Short Program on Riemannian Geometry,'' a workshop held at the CRM in Montreal in 2004. It will be a valuable reference for graduate students and research mathematicians alike. Information for our distributors: Titles inthis series are copublished with the Centre de Recherches Mathematiques.
Large Deviations
Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.
Introduction to Homotopy Theory
Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
