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The geometry of laminations

100%

Fokkink R. J., Oversteegen L. G.

Fundamenta Mathematicae

1996

tom 151

nr 3

195-207

A lamination is a continuum which locally is the product of a Cantor set and an arc. We investigate the topological structure and embedding properties of laminations. We prove that a nondegenerate lamination cannot be tree-like and that a planar lamination has at least four complementary domains. Furthermore, a lamination in the plane can be obtained by a lakes of Wada construction.

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Speeds of convergence of orbits of non-elliptic semigroups of holomorphic self-maps of the unit disk

100%

Bracci F.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2019

tom 73

nr 2

We introduce three quantities related to orbits of non-elliptic continuous semigroups of holomorphic self-maps of the unit disk, the total speed, the orthogonal speed, and the tangential speed and show how they are related and what can be inferred from those.

Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold

51%

Toda M.

Open Mathematics

2004

tom 2

nr 2

218-249

The paper studies the first homology of finite regular branched coverings of a universal Borromean orbifold called B 4,4,4ℍ3. We investigate the irreducible components of the first homology as a representation space of the finite covering transformation group G. This gives information on the first betti number of finite coverings of general 3-manifolds by the universality of B 4,4,4. The main result of the paper is a criterion in terms of the irreducible character whether a given irreducible representation of G is an irreducible component of the first homology when G admits certain symmetries. As a special case of the motivating argument the criterion is applied to principal congruence subgroups of B 4,4,4. The group theoretic computation shows that most of the, possibly nonprincipal, congruence subgroups are of positive first Betti number.

Ograniczanie wyników

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Fundamenta Mathematicae

1 Open Mathematics

1 Bracci F.

1 Fokkink R. J.

1 Oversteegen L. G.

1 Toda M.

1 2019

1 2004

1 1996

Wyniki wyszukiwania

The geometry of laminations

Speeds of convergence of orbits of non-elliptic semigroups of holomorphic self-maps of the unit disk

Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold