Одновимірні шарування на поверхнях та їх простори листів

Abstract

The work is of an overview nature. A class of striped surfaces is considered: two-dimensional surfaces that can be glued from horizontal strips and on which one-dimensional canonical foliation is defined in a certain way. A number of combinatorial and homotopy invariants for surfaces of this class are considered. Necessary and sufficient conditions are given under which a two-dimensional manifold M 2 on which a one-dimensional foliation ∆ is given, each leaf of which is homeomorphic to R1 and is a closed subset of M 2 , is homeomorphic to some striped surface.