Enrique Ramírez-Losada

The trefoil knot is as universal as it can be

Abstract Let τ p , q ⊂ S 3 denote the p , q -torus knot. It is known that if ϕ :M→S 3 is a branched covering branched along τ p , q , then M is an orientable Seifert manifold with orientable base and non-zero Euler number. We prove a converse of this fact: If M is an orientable Seifert manifold with orientable base and non-zero Euler number, M is a branched covering of S 3 with branching along the knot τ p , q for any p , q , ( p , q )=1, and 2⩽ p q . As an application of our techniques we compute, in terms of Seifert invariants, the cyclic branched coverings of S 3 branched along τ p , q .

Meridional surfaces and (1,1)-knots

We determine all (1,1)-knots which admit an essential meridional surface, namely, we give a construction which produces (1,1)-knots having essential meridional surfaces, and show that if a (1,1)-knot admits an essential meridional surface, then it comes from the given construction.

Hyperbolic (1,2)-knots in S3 with crosscap number two and tunnel number one

Abstract A knot in S 3 is said to have crosscap number two if it bounds a once-punctured Klein bottle but not a Moebius band. In this paper we give a method of constructing crosscap number two hyperbolic ( 1 , 2 ) -knots with tunnel number one which are neither 2-bridge nor ( 1 , 1 ) -knots. An explicit infinite family of such knots is discussed in detail.

Coverings of torus knots in S2 × S1 and universals

Let

Circular handle decompositions of free genus one knots

t_{\alpha,\beta}\subset S^2\times S^1

ON UNIVERSAL KLEINIAN GROUPS GENERATED BY 180 ◦ ROTATIONS

be an ordinary fiber of a Seifert fibering of

Once-punctured Klein bottles in knot complements

S^2\times S^1

Genera of coverings of torus bundles

with two exceptional fibers of order

Classification of genus two knots which admit a (1,1)-decomposition

\alpha

Coverings of torus knots in

. We show that any Seifert manifold with Euler number zero is a branched covering of