2019
Том 71
№ 11

All Issues

Homeotopy groups for nonsingular foliations of the plane

Soroka Yu. Yu.

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Abstract

We consider a special class of nonsingular oriented foliations $F$ on noncompact surfaces $\Sigma$ 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 $\Sigma$ mapping the leaves onto leaves and preserving their orientations. Also let $K$ be the group of homeomorphisms of the quotient space $\Sigma /F$ 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 $\pi_ 0K = K/K_0$.

Citation Example: Soroka Yu. Yu. Homeotopy groups for nonsingular foliations of the plane // Ukr. Mat. Zh. - 2017. - 69, № 7. - pp. 1000-1008.

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