Geodesic
On the possibility of constructing a curve for a given group of homeomorphisms
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 218-229 Cet article a éte moissonné depuis la source Math-Net.Ru

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The following problem is considered: for a given group of homeomorphisms of a topological space, it is required to determine if there exists in this space a curve for which the given group is a group of oriented homeomorphisms. A constructive solution of the problem is given for a wide class of groups of homeomorphisms of linearly connected topological spaces. In a number of cases, the questions on the uniqueness of the constructed curve and on the kernel of action of the group on the curve are investigated.
Keywords: curve, image of a curve, topological space, group of homeomorphisms, linear connectivity. 
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E. A. Rogozinnikov. On the possibility of constructing a curve for a given group of homeomorphisms. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 218-229. http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a25/

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