Homeotopy groups for nonsingular foliations of the plane
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 p...
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| Date: | 2017 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2017
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1753 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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 $\pi_ 0K = K/K_0$. |
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