Related papers: On the existence of universal links in three-manif…

For $m=2$ and $m=3$ we prove that any connected, oriented, open manifold $M^m$ admits a simple branched covering map over $\mathbb{R}^m$. When $M$ has $k$ ends and $k$ is finite, the degree of the cover can be taken to be $mk$. Regardless…

One method for obtaining every closed orientable 3-manifold is as branched covering of the 3-sphere over a link. There is a classical topological result showing that the minimun possible number of sheets in the covering is three. In this…

We show that there exists a transverse link in the standard contact structures on the 3-sphere such that all contact 3-manifolds are contact branched covers over this transverse link.

Given a real analytic function $f$ from $\mathbb{R}^4$ to $\mathbb{R}^2$ with isolated critical point at the origin, the link $L_f$ of the singularity is a real fibred knot in $\mathbb{S}^{3}$. From this singularities, we construct a family…

It is shown that every knot or link is the set of complex tangents of a 3-sphere smoothly embedded in the three-dimensional complex space. We show in fact that a one-dimensional submanifold of a closed orientable 3-manifold can be realised…

For a closed 3-manifold $M$ in a certain class, we give a presentation of the cellular chain complex of the universal cover of $M$. The class includes all surface bundles, some surgeries of knots in $S^3$, some cyclic branched cover of…

Let $M$ be a connected, closed, oriented three-manifold and $K$, $L$ two rationally null-homologous oriented simple closed curves in $M$. We give an explicit algorithm for computing the linking number between $K$ and $L$ in terms of a…

We show that any open aspherical manifold of dimension n>3 is tangentially homotopy equivalent to an n-manifold whose universal cover is not homeomorphic to the Euclidean space.

In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is…

An irreducible open 3-manifold $W$ is {\bf R}$^2$-irreducible if every proper plane in $W$ splits off a halfspace. In this paper it is shown that if such a $W$ is the universal cover of a connected, {\bf P}$^2$-irreducible open 3-manifold…

We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions.…

Suppose $M$ is a closed, connected, orientable, \irr\ \3m\ such that $G=\pi_1(M)$ is infinite. One consequence of Thurston's geometrization conjecture is that the universal covering space $\widetilde{M}$ of $M$ must be \homeo\ to $\RRR$.…

It is natural to ask how many isotopy classes of embedded essential surfaces lie in a given 3-manifold. The first bounds on the number of such surfaces were exponential, using normal surfaces. More recently, by restricting to alternating…

M. Freedman and V. Krushkal introduced the notion of a "filling" link in a 3-manifold: a link $L$ is filling in $M$ if for any spine $G$ of $M$ disjoint from $L$, $\pi_1(G)$ injects into $\pi_1(M \setminus L )$. Freedman and Krushkal show…

We show that a hyperbolic $3$-manifold can be the cyclic branched cover of at most fifteen knots in $\mathbf{S}^3$. This is a consequence of a general result about finite groups of orientation preserving diffeomorphisms acting on…

There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of $n$-fold coverings over orientable Euclidean manifolds…

We consider closed acylindrical surfaces in 3-manifolds and in knot and link complements, and show that the genus of these surfaces is bounded linearly by the number of tetrahedra in the triangulation of the manifold and by the number of…

We prove that there is a knot $K$ transverse to $\xi_{std}$, the tight contact structure of $S^3$, such that every contact 3-manifold $(M, \xi)$ can be obtained as a contact covering branched along $K$. By contact covering we mean a map…

Examples suggest that there is a correspondence between L-spaces and 3-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions for several large classes of such manifolds. In…

We show that only finitely many links in a closed 3-manifold share the same complement, up to twists along discs and annuli. Using the same techniques, we prove that by adding 2-handles on the same link we get only finitely many smooth…