We consider a special class of nonsingular oriented foliations F on noncompact surfaces Σ whose spaces of leaves have a 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. In addition, 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 \( {\pi}_0{H}^{+}(F)={H}^{+}(F)/{H}_0^{+}(F) \) and π 0 K = K/K 0 .
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 7, pp. 1000–1008, July, 2017.
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Soroka, Y.Y. Homeotopy Groups for Nonsingular Foliations of the Plane. Ukr Math J 69, 1164–1174 (2017). https://doi.org/10.1007/s11253-017-1423-6
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DOI: https://doi.org/10.1007/s11253-017-1423-6