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# Homeotopy groups of rooted tree like non-singular foliations on the plane

### Abstract

Let $F$ be a non-singular foliation on the plane with all leaves being closed subsets, $H^{+}(F)$ be the group of homeomorphisms of the plane which maps leaves onto leaves endowed with compact open topology, and $H^{+}_{0}(F)$ be the identity path component of $H^{+}(F)$. The quotient $\pi_0 H^{+}(F) = H^{+}(F)/H^{+}_{0}(F)$ is an analogue of a mapping class group for foliated homeomorphisms. We will describe the algebraic structure of $\pi_0 H^{+}(F)$ under an assumption that the corresponding space of leaves of $F$ has a structure similar to a rooted tree of finite diameter.

Key words: Non-singular foliations, homeotopy groups.

### Article Information

 Title Homeotopy groups of rooted tree like non-singular foliations on the plane Source Methods Funct. Anal. Topology, Vol. 22 (2016), no. 3, 283-294 MathSciNet MR3554654 zbMATH 06742112 Milestones Received 31/03/2016 Copyright The Author(s) 2016 (CC BY-SA)

### Authors Information

Yu. Yu. Soroka
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

### Citation Example

Yu. Yu. Soroka, Homeotopy groups of rooted tree like non-singular foliations on the plane, Methods Funct. Anal. Topology 22 (2016), no. 3, 283-294.

### BibTex

@article {MFAT894,
AUTHOR = {Yu. Yu. Soroka},
TITLE = {Homeotopy groups of rooted tree like non-singular foliations on the plane},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {22},
YEAR = {2016},
NUMBER = {3},
PAGES = {283-294},
ISSN = {1029-3531},
MRNUMBER = {MR3554654},
ZBLNUMBER = {06742112},
URL = {http://mfat.imath.kiev.ua/article/?id=894},
}

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