Overview:Topology of Closed One-forms - Mathematical Surveys and Monographs - This monograph is an introduction to the fascinating field of the topology, geometry and dynamics of closed one-forms. The subject was initiated by S. P. Novikov in 1981 as a study of Morse type zeros of closed one-forms. The first two chapters of the book, written in textbook style, give a detailed exposition of Novikov theory, which plays a fundamental role in geometry and topology. Subsequent chapters of the book present a variety of topics where closed one-forms play a central role. The most significant results are the following: the solution of the problem of exactness of the Novikov inequalities for manifolds with the infinite cyclic fundamental group; the solution of a problem raised by E. Calabi about intrinsically harmonic closed one-forms and their Morse numbers; and, the construction of a universal chain complex which bridges the topology of the underlying manifold with information about zeros of closed one-forms.This complex implies many interesting inequalities including Bott-type inequalities, equivariant inequalities, and inequalities involving von Neumann Betti numbers. The construction of a novel Lusternik-Schnirelman-type theory for dynamical systems. Closed one-forms appear in dynamics through the concept of a Lyapunov one-form of a flow. As is shown in the book, homotopy theory may be used to predict the existence of homoclinic orbits and homoclinic cycles in dynamical systems ('focusing effect').
This book is on page /0fb06c92acf561788291222b8bb2eff7/book/1603729811-9780821835319. It was written by the following authors: . Book Topology of Closed One-forms - Mathematical Surveys and Monographs, which can be read online, published by the company: American Mathematical Society. Other books on similar topics can be found in sections: Medicine, Technology, Science. The book was published on 2004-02-29. File for download Topology of Closed One-forms - Mathematical Surveys and Monographs has PDF format and is called topology-of-closed-one-forms-mathematical-surveys-and-monographs.pdf. Other books you can download below. Our poumm.fr site is not responsible for the content of PDF files.
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