The Tangent cone of an Aleksandrov space of curvature.
The Poincaré-Bendixson theorem and arational foliations on the sphere
Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.
-algebras and topology of mapping tori
The paper studies applications of -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension , and . In conclusion, we consider two numerical examples illustrating our main results.
On a Teichmüller functor between the categories of complex tori and the Effros-Shen algebras.
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