Homeotopy groups of one-dimensional foliations on surfaces
| dc.contributor.author | Сергій Іванович Максименко, Євген Олександрович Полулях, Юлія Юріївна Сорока | |
| dc.date.accessioned | 2018-12-19T12:54:57Z | |
| dc.date.available | 2018-12-19T12:54:57Z | |
| dc.date.issued | 2017 | |
| dc.description.abstract | Let $Z$ be a non-compact two-dimensional manifold obtained from a family of open strips $mathbb{R}times(0,1)$ with boundary intervals by gluing those strips along their boundary intervals.Every such strip has a foliation into parallel lines $mathbb{R}times t$, $tin(0,1)$, and boundary intervals, whence we get a foliation $Delta$ on all of $Z$.Many types of foliations on surfaces with leaves homeomorphic to the real line have such ``striped'' structure.That fact was discovered by W.~Kaplan (1940-41) for foliations on the plane $mathbb{R}^2$ by level-set of pseudo-harmonic functions $mathbb{R}^2 to mathbb{R}$ without singularities. Previously, the first two authors studied the homotopy type of the group $mathcal{H}(Delta)$ of homeomorphisms of $Z$ sending leaves of $Delta$ onto leaves, and shown that except for two cases the identity path component $mathcal{H}_{0}(Delta)$ of $mathcal{H}(Delta)$ is contractible.The aim of the present paper is to show that the quotient $mathcal{H}(Delta)/ mathcal{H}_{0}(Delta)$ can be identified with the group of automorphisms of a certain graph with additional structure encoding the ``combinatorics'' of gluing. | |
| dc.identifier.issn | 2409-8906 | |
| dc.identifier.uri | https://card-file.ontu.edu.ua/handle/123456789/6223 | |
| dc.identifier.uri | https://doi.org/10.15673/tmgc.v1i10.548 | |
| dc.source | Proceedings of the International Geometry Center | |
| dc.title | Homeotopy groups of one-dimensional foliations on surfaces |