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


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.

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

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

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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.


@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 = {},


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