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Displaying 21 – 37 of 37

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

Masahito Toda (2004)

Open Mathematics

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...

Representations of (1,1)-knots

Alessia Cattabriga, Michele Mulazzani (2005)

Fundamenta Mathematicae

We present two different representations of (1,1)-knots and study some connections between them. The first representation is algebraic: every (1,1)-knot is represented by an element of the pure mapping class group of the twice punctured torus PMCG₂(T). Moreover, there is a surjective map from the kernel of the natural homomorphism Ω:PMCG₂(T) → MCG(T) ≅ SL(2,ℤ), which is a free group of rank two, to the class of all (1,1)-knots in a fixed lens space. The second representation is parametric: every...

Representations of orbifold groups and parabolic bundles.

Hans U. Boden (1991)

Commentarii mathematici Helvetici

Representing 3-manifolds by triangulations of $S^{3}$ . I: A constructive approach.

Hilden, Mike, Montesinos, José M., Tejada, Débora, Toro, Margarita (2005)

Revista Colombiana de Matemáticas

Representing Countable Groups by Homeomorphism Groups in Hilbert Space.

Jan van Mill (1982)

Mathematische Annalen

Representing open 3-manifolds as 3-fold branched coverings.

José María Montesinos-Amilibia (2002)

Revista Matemática Complutense

It is proved that the Freudenthal compactification of an open, connected, oriented 3-manifold is a 3-fold branched covering of S3, and in some cases, a 2-fold branched covering of S3. The branching set is a locally finite disjoint union of strings.

Reshetikhin-Turaev invariants of Seifert 3-manifolds and a rational surgery formula.

Hansen, Søren Kold (2001)

Algebraic & Geometric Topology

Residual Finiteness of Surface Groups via Tessellations.

L.M. Lopez (1994)

Discrete & computational geometry

Residual sets not of maximum dimension

D. A. Moran (1973)

Colloquium Mathematicae

Resolutions of Homology Manifolds, and the Topological Characterization of Manifolds.

Frank Quinn (1983)

Inventiones mathematicae

Riemannian $L^{p}$ structures and $K$ -homology. (Structures riemanniennes $L^{p}$ et $K$ -homologie.)

Hilsum, Michel (1999)

Annals of Mathematics. Second Series

Rigid sets in manifolds

David G. Wright (1986)

Banach Center Publications

Rigidity of cusps in deformations of hyperbolic 3-orbifolds.

Walter D. Neumann, Alan W. Reid (1993)

Mathematische Annalen

Rigidity of Rank-One Factors of Compact Symmetric Spaces

Andrew Clarke (2011)

Annales de l’institut Fourier

We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.

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