2017
Том 69
№ 9

All Issues

Homeotopy groups for nonsingular foliations of the plane

Soroka Yu. Yu.


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 $H^+(F)$ and K0 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 $\pi 0K = KK_0$.

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