Yu. Yu. Soroka

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Articles: 2

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

Yu. Yu. Soroka

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 22 (2016), no. 3, 283-294

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.

Topological equivalence to a projection

V. V. Sharko, Yu. Yu. Soroka

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 21 (2015), no. 1, 3-5

We present a necessary and sufficient condition for a continuous function on a plane to be topologically equivalent to a projection onto one of the coordinates.

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