Displaying similar documents to “On the disc theorem”

Realization of primitive branched coverings over closed surfaces following the hurwitz approach

Semeon Bogatyi, Daciberg Gonçalves, Elena Kudryavtseva, Heiner Zieschang (2003)

Open Mathematics

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Let V be a closed surface, H⊑π1(V) a subgroup of finite index l and D=[A 1,...,A m] a collection of partitions of a given number d≥2 with positive defect v(D). When does there exist a connected branched covering f:W→V of order d with branch data D and f∶W→V It has been shown by geometric arguments [4] that, for l=1 and a surface V different from the sphere and the projective plane, the corresponding branched covering exists (the data D is realizable) if and only if the data D fulfills...

A topological version of Bertini's theorem

Artur Piękosz (1995)

Annales Polonici Mathematici

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We give a topological version of a Bertini type theorem due to Abhyankar. A new definition of a branched covering is given. If the restriction π V : V → Y of the natural projection π: Y × Z → Y to a closed set V ⊂ Y × Z is a branched covering then, under certain assumptions, we can obtain generators of the fundamental group π₁((Y×Z).

An infinitary version of Sperner's Lemma

Aarno Hohti (2006)

Commentationes Mathematicae Universitatis Carolinae

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We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.