Описание: This is the first systematic and self-contained textbook on homotopy methods in the study of periodic points of a map. A modern exposition of the classical topological fixed-point theory with a complete set of all the necessary notions as well as new proofs of the Lefschetz-Hopf and Wecken theorems are included. Periodic points are studied through the use of Lefschetz numbers of iterations of a map and Nielsen-Jiang periodic numbers related to the Nielsen numbers of iterations of this map. Wecken theorem for periodic points is then discussed in the second half of the book and several results on the homotopy minimal periods are given as applications, e.g. a homotopy version of the Г…arkovsky theorem, a dynamics of equivariant maps, and a relation to the topological entropy. Students and researchers in fixed point theory, dynamical systems, and algebraic topology will find this text invaluable.
Описание: The main aim of this text is to introduce the beginner to the theory of topological rings. Whilst covering all the essential theory of topological groups, the text focuses on locally compact, compact, linearly compact, hereditarily linear compact and bounded topological rings. The text also contains new, unpublished results on topological rings, for example the nilideals of topological rings, trivial extensions of special type, rings with a unique compact topology, compact right topological rings and the results from groups of units of topological rings.
Автор: Arnold Название: Topological Methods in Hydrodynamics ISBN: 038794947X ISBN-13(EAN): 9780387949475 Издательство: Springer Рейтинг: Цена: 12154 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Topological hydrodynamics is a young branch of mathematics studying topological features of flows with complicated trajectories, as well as their applications
to fluid motions. It is situated at the crossroad of hyrdodynamical stability theory, Riemannian and symplectic geometry, magnetohydrodynamics, theory of Lie algebras and Lie groups,
knot theory, and dynamical systems. Applications of this approach include topological classification of steady fluid flows, descriptions of the Korteweg-de Vries equation as a geodesic
flow, and results on Riemannian geometry of diffeomorphism groups, explaining, in particular, why longterm dynamical weather forecasts are not reliable.
in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics for a unified point of view. T
e necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is accessible to graduate students as well as
to both pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems and differential geometry.
Описание: "Topological Foundations of Electromagnetism" seeks a fundamental understanding of the dynamics of electromagnetism; and marshals the evidence that in
certain precisely defined topological conditions, electromagnetic theory (Maxwell's theory) must be extended or generalized in order to provide an explanation and understanding of, until
now, unusual electromagnetic phenomena. The key to this generalization is an understanding of the circumstances under which the so-called A potential fields have physical
effects.Basic to the approach taken is that the topological composition of electromagnetic fields is the fundamental conditioner of the dynamics of these fields. The treatment of
electromagnetism from, first, a topological perspective, continuing through group theory and gauge theory, to a differential calculus description is a major thread of the book.
Suggestions for potential new technologies based on this new understanding and approach to conditional electromagnetism are also given.
Описание: This book provides a comprehensive overview of the authors' pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage
includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and
applications to best approximation theory, partial equations and boundary value problems. Self-contained and unified in presentation, the book considers the existence of equilibrium
points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities.
It also provides the latest developments in KKM theory and
degree theory for nonlinear set-valued mappings.
Описание: This is the first of three volumes collecting the original and now classic works in topology written in the 50s-60s. The original methods and constructions from
these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that
is, from Serre's celebrated "Singular homologies of fibre spaces." This is the translation of the Russian edition published in 2005 with one entry (Milnor's lectures on the h-cobordism)
Описание: ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 14 18, 2002 at Taiyuan, Shanxi Province, China. This conference was
organized by Mathematical School of Peking University, Academy of Ma
hematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored
by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. Attending the conference were 166 mathematicians from 21 countries and areas
in the world with 53 invited speakers and 30 contributors presenting their lectures.
This conference aims at an overview of the recent development in nonlinear analysis. It
covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrodinger equations, semilinear elliptic
equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.
Описание: "The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory . . . reading is fluid and very pleasant . . . style is informal but far from being imprecise." вЂ”MATHEMATICAL REVIEWS (Review of the First Edition) Here is a book that will be a joy to the mathematician or graduate student of mathematics---or even the well-prepared undergraduate---who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world.New to the second edition: New chapters will supply additional applications of the theory and techniques presented in the book. * Several new proofs, making the second edition more self-contained.
Описание: This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field
theory. These include: Hopf algebras underlying renormalization schemes in quantum field theory; noncommutative geometry with applications to index theory on one hand and the study
of aperiodic solids on the other; geometry and topology of low dimensional manifolds with applications to topological field theory; Chern-Simons supergravity; and the anti de
Sitter/conformal field theory correspondence. The volume comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by
supergravity and string theory, complemented by some short communications by young participants of the school.
Описание: This book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.
Автор: Efton Park Название: Complex Topological K-Theory ISBN: 0521856345 ISBN-13(EAN): 9780521856348 Издательство: Cambridge Academ Рейтинг: Цена: 5933 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students new to the subject. No background in algebraic topology is assumed; the reader need only have taken the standard first courses in real analysis, abstract algebra, and point-set topology. The book begins with a detailed discussion of vector bundles and related algebraic notions, followed by the definition of K-theory and proofs of the most important theorems in the subject, such as the Bott periodicity theorem and the Thom isomorphism theorem. The multiplicative structure of K-theory and the Adams operations are also discussed and the final chapter details the construction and computation of characteristic classes. With every important aspect of the topic covered, and exercises at the end of each chapter, this is the definitive book for a first course in topological K-theory.
Автор: A. A. Ranicki Название: Algebraic L-theory and Topological Manifolds ISBN: 0521055210 ISBN-13(EAN): 9780521055215 Издательство: Cambridge Academ Рейтинг: Цена: 5204 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents a definitive account of the applications of the algebraic L-theory to the surgery classification of topological manifolds. The central result is the identification of a manifold structure in the homotopy type of a Poincare duality space with a local quadratic structure in the chain homotopy type of the universal cover. The difference between the homotopy types of manifolds and Poincare duality spaces is identified with the fibre of the algebraic L-theory assembly map, which passes from local to global quadratic duality structures on chain complexes. The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance of the higher signatures; any other formulation necessarily factors through this one. The book is designed as an introduction to the subject, accessible to graduate students in topology; no previous acquaintance with surgery theory is assumed, and every algebraic concept is justified by its occurrence in topology.
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