HOMEOTOPY GROUPS OF ROOTED TREE LIKE NON-SINGULAR FOLIATIONS ON THE PLANE

Let F be a non-singular foliation on the plane with all leaves being closed subsets, H+ (F) be the group of homeomorphisms of the plane which maps leaves onto leaves endowed with compact open topology, and Ho (F) be the identity path component of H+ (F). The quotient pi H-0(+) (F) = H+ (F)/H-0(+) (F) is an analogue of a mapping class group for foliated homeomorphisms. We will describe the algebraic structure of pi H-0(+) (F) under an assumption that the corresponding space of leaves of F has a structure similar to a rooted tree of finite diameter.