Topology of Closed One-forms - Mathematical Surveys and Monographs (Hardback)
  • Topology of Closed One-forms - Mathematical Surveys and Monographs (Hardback)
zoom

Topology of Closed One-forms - Mathematical Surveys and Monographs (Hardback)

£78.50
Hardback Published: 29/02/2004
  • We can order this

Usually despatched within 3 weeks

  • This item has been added to your basket
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').

Publisher: American Mathematical Society
ISBN: 9780821835319
Weight: 669 g
Dimensions: 230 x 189 x 18 mm

You may also be interested in...

Modern Graph Theory
Added to basket
Knots
Added to basket
£16.95
Paperback
Introduction to Topology
Added to basket
Riemann Surfaces
Added to basket
Metric Spaces
Added to basket
A Combinatorial Introduction to Topology
Added to basket
Essential Topology
Added to basket
Schaums Outline of General Topology
Added to basket
Algebraic Topology
Added to basket
£30.99
Paperback
Knot Theory and Its Applications
Added to basket
Fractals: A Very Short Introduction
Added to basket

Reviews

Please sign in to write a review

Your review has been submitted successfully.