{"product_id":"topology-of-closed-one-forms","title":"Topology of Closed One-forms","description":"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').","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":57230460518744,"sku":"9780821835319","price":122.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9780821835319_354cb8aa-d013-4887-a749-450fccaf45e5.jpg?v=1780114568","url":"https:\/\/agendabookshop.com\/products\/topology-of-closed-one-forms","provider":"Agenda Bookshop","version":"1.0","type":"link"}