Viewed locally, a closed one-form on a manifold is a smooth function up to an additive constant. The global structure of a closed one-form is mainly determined by its de Rham cohomology class. In this book, Michael Farber studies fascinating geometrical, topological, and dynamical properties of closed one-forms. In particular, he reveals the relations between their global and local features. In 1981, S. P. Novikov initiated a generalization of Morse theory in which, instead of critical points of smooth functions, one deals with closed one-forms and their zeros. The first two chapters of the...
Viewed locally, a closed one-form on a manifold is a smooth function up to an additive constant. The global structure of a closed one-form is mainly d...
