# Foliations with all non-closed leaves on non-compact surfaces

@article{Maksymenko2016FoliationsWA, title={Foliations with all non-closed leaves on non-compact surfaces}, author={Sergiy Ivanovych Maksymenko and Eugene Polulyakh}, journal={arXiv: Geometric Topology}, year={2016} }

Let $X$ be a connected non-compact $2$-dimensional manifold possibly with boundary and $\Delta$ be a foliation on $X$ such that each leaf $\omega\in\Delta$ is homeomorphic to $\mathbb{R}$ and has a trivially foliated neighborhood. Such foliations on the plane were studied by W. Kaplan who also gave their topological classification. He proved that the plane splits into a family of open strips foliated by parallel lines and glued along some boundary intervals. However W. Kaplan's construction… Expand

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