Marco Reni

Twofold unbranched coverings of genus two 3-manifolds are hyperelliptic

A closed 3-dimensional manifold is hyperelliptic if it admits an involution such that the quotient space of the manifold by the action of the involution is homeomorphic to the 3-sphere. We prove that a twofold unbranched covering of a genus two 3-manifold is hyperelliptic. This result is reminiscent of a theorem, which seems to have first appeared in a paper by Enriques and which has been reproved more recently by Farkas and Accola, which states that a twofold unbranched covering of a Riemann surface of genus two is hyperelliptic.

Hyperbolic 3-manifolds as cyclic branched coverings

Abstract. There is an extensive literature on the characterization of knots in the 3-sphere which have the same 3-manifold as a common n-fold cyclic branched covering, for some integer

Isometry Groups of Hyperbolic Three-Manifolds which are Cyclic Branched Coverings

n \ge 2

Handlebody orbifolds and Schottky uniformizations of hyperbolic 2-orbifolds

. In the present paper, we study the following more general situation. Given two integers m and n, how are knots K1 and K2 related such that the m-fold cyclic branched covering of K1 coincides with the n-fold cyclic branched covering of K2. Or, seen from the point of view of 3-manifolds: in how many different ways can a given 3-manifold occur as a cyclic branched covering of knots in S3. Under certain hypotheses, we solve this problem for the basic class of hyperbolic 3-manifolds and hyperbolic knots (the other basic class is that of Seifert fiber spaces resp. of torus and Montesinos knots for which the situation is well understood; the general case can then be analyzed using the equivariant sphere and torus decomposition into Seifert fiber spaces and hyperbolic manifolds).

Hyperbolic links and cyclic branched coverings

AbstractLet M be a hyperbolic three-manifold which is an n-fold cyclic branched covering of a hyperbolic link L in the three-sphere, or more precisely, of the hyperbolic three-orbifold

Dihedral Branches Coverings of Hyperbolic Orbifolds

\mathcal{O}_n (L)

Cyclic actions on compression bodies

whose underlying topological space is the three-sphere and whose singular set, of branching index n, the link L. We say that M has no hidden symmetries (with respect to the given branched covering) if the isometry group of M is the lift of (a subgroup of) the isometry group of the hyperbolic orbifold