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Bundles, connections, metrics & curvature are the lingua franca of modern differential geometry & theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, & providing numerous examples, the book would suit a on...e-semester course on the subject of bundles & the associated geometry
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An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the ess...ential mathematical methods and tools.
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Innovative methods for the analysis of chaotic systems, in this second edition completed by a broad introduction for the non expert, additional chapters on embeddings, bounding tori, and the representation theory for strange attractors, and frequently asked questions.
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A timely graduate level text in an active field covering functional analysis, with an emphasis on Banach algebras.
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This book covers important topics involving topological methods in the theory of systems of differential equations (DE's). The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control... theory. Since the dynamics of economical, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis. In this book, the authors present the essential background in multivalued analysis, before developing ideas such as Vietoris topology, a variety of fixed point theorems including those of Kakutani, Fan, Leray and Schauder and systems of impulsive DE's.
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Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs). Ocneanu, in particular, showed that subfactors yield TQFTs that complement the Turaev-Viro construction. Until now, however, it has been difficult to find an account of th...is work that is both detailed and accessible. Topological Quantum Field Theories from Subfactors provides a self-contained, explicit description of Ocneanu's construction It introduces and discusses its various ingredients with the distinct advantage of employing only genuine triangulations. The authors begin with axioms for a TQFT, go through the Turaev-Viro prescription for constructing such a TQFT, and finally work through Ocneanu's method of starting with a finite depth hyperfinite subfactor and obtaining the data needed to invoke the Turaev-Viro machine. The authors provide a very concise treatment of finite factors of type and their bimodules and include details and calculations for all constructions. They also present, perhaps for the first time in book form, notions such as quantization functors and fusion algebras. Accessible to graduate students and others just beginning to explore this intriguing topic, Topological Quantum Field Theories from Subfactors will also be of interest to researchers in both mathematics and theoretical physics.
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The description for this book, Foundations of Algebraic Topology, will be forthcoming.
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The description for this book, Topological Analysis, will be forthcoming.
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Group actions are an efficient way of describing symmetries in objects by defining the essential elements of a given object as a set. The symmetries of the object are then defined as the symmetry group of this set. This title explores group actions on the simplest closed manifold..., the circle.
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The description for this book, The Seduction of Curves, will be forthcoming.
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