Homeotopy groups for nonsingular foliations of the plane - Soroka, Yu. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We consider a special class of nonsingular oriented foliations F on noncompact surfaces Σ whose spaces of leaves have the structure similar to the structure of rooted trees of finite diameter. Let H^+(F) be the group of all homeomorphisms of Σ mapping the leaves onto leaves and preserving their orientations. Also let K be the group of homeomorphisms of the quotient space Σ /F induced by H^+(F). By H^+_0(F) and K_0 we denote the corresponding subgroups formed by the homeomorphisms isotopic to identity mappings. Our main result establishes the isomorphism between the homeotopy groups π_0 H^+(F) = H^+(F)/H^+ _0 (F) and π_ 0K = K/K_0.