|
|
libcats.org
Topology of Closed One-FormsMichael FarberThis 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. 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'''').
Популярные книги за неделю:
Система упражнений по развитию способностей человека (Практическое пособие)Автор: Петров Аркадий НаумовичКатегория: Путь к себе
Размер книги: 818 Kb
Сотворение мира (3-х томник)Автор: Петров Аркадий НаумовичКатегория: Путь к себе
Размер книги: 817 Kb
Только что пользователи скачали эти книги:
Practical Machinery Vibration Analysis and Predictive MaintenanceАвтор: Paresh Girdhar
Размер книги: 12.18 Mb
Advances in Natural Language Processing 4 confАвтор: José Luis Vicedo, Автор: Particio Martínez-Barco, Автор: Rafael Munoz, Автор: Maximiliano Saiz NoedaКатегория: Cs_Computer science, CsLn_Lecture notes
Размер книги: 4.31 Mb
Solution Manual to options futures and other derivativesАвтор: John Hull, Автор: John C. HullКатегория: Chemistry-Environmental-Material
Размер книги: 13.05 Mb
Who's who in economicsАвтор: Mark Blaug, Автор: Howard R. VaneКатегория: Экономика и финансы
Размер книги: 7.89 Mb
It's All About the Bike: The Pursuit of Happiness on Two WheelsАвтор: Robert Penn
Размер книги: 3.77 Mb
Religion and Law in Classical and Christian Rome (Potsdamer Altertumswissenschaftliche Beiträge (PAwB))Автор: Clifford Ando, Автор: Jörg Rüpke (eds.)
Размер книги: 4.01 Mb
|
|
|