Homeotopy groups of rooted tree like non-singular foliations on the plane - Soroka, Yu. Yu. (Methods of Functional Analysis and Topology, 2016)
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 H^+_0(F) be the identity path component of H^+(F). The quotient π_0 H^+(F) = H^+(F)/H^+_0(F) is an analogue of a mapping class group for foliated homeomorphisms. We will describe the algebraic structure of π_0 H^+(F) under an assumption that the corresponding space of leaves of F has a structure similar to a rooted tree of finite diameter.