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.

Published in Methods of Functional Analysis and Topology (MFAT), available at http://mfat.imath.kiev.ua/article/?id=894

Cited by in corpus (1)

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