TY - BOOK ID - 5406986 TI - Circle-valued Morse theory PY - 2006 VL - 32 SN - 1282194267 9786612194269 3110197979 3110158078 9783110158076 9783110197976 PB - Berlin New York De Gruyter DB - UniCat KW - Manifolds (Mathematics). KW - Mathematics. KW - Morse theory. KW - Morse theory KW - Manifolds (Mathematics) KW - Morse, théorie de KW - Variétés (Mathématiques) KW - Geometry, Differential KW - Topology KW - Calculus of variations KW - Critical point theory (Mathematical analysis) KW - Differential geometry. UR - https://www.unicat.be/uniCat?func=search&query=sysid:5406986 AB - In the early 1920's M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. Circle-valued Morse theory originated from a problem in hydrodynamics studied by S. P. Novikov in the early 1980's. Nowadays, it is a constantly growing field of contemporary mathematics with applications and connections to many geometrical problems such as Arnold's conjecture in the theory of Lagrangian intersections, fibrations of manifolds over the circle, dynamical zeta functions, and the theory of knots and links in the three-dimensional sphere. The aim of the book is to give a systematic treatment of geometric foundations of the subject and recent research results. The book is accessible to first year graduate students specializing in geometry and topology. ER -