Related papers: Virtual domination of 3-manifolds II

In this paper, it is shown that every orientable closed 3-manifold maps with nonzero degree onto at most finitely many homeomorphically distinct irreducible non-geometric orientable closed 3-manifolds. Moreover, given any nonzero integer,…

A new direct proof of the Virtual Haken Conjecture, which asserts that every compact, orientable, irreducible three-dimensional manifold with infinite fundamental group has a finite cover that is Haken, will be given.

We give an upper bound for the number of compact essential orientable non-isotopic surfaces, with Euler characteristic at least some constant $\chi$, properly embedded in a finite-volume hyperbolic 3-manifold $M$, closed or cusped. This…

This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This technique is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new…

For any hyperbolic 3-manifold $M$ with totally geodesic boundary, there are finitely many boundary slopes for essential immersed surfaces of a given genus. There is a uniform bound for the number of such boundary slopes if the genus of…

We prove that given two compact oriented $3$-manifolds $N$ and $M,$ with $M$ satisfying only a mild hypothesis, there is a hyperbolic $3$-manifold $N'$ arbitrarily ``closely related'' to $N,$ and such that $N'$ does not embed in $M.$ For…

In this paper, we will use Kahn-Markovic's almost totally geodesic surfaces to construct certain $\pi_1$-injective 2-complexes in closed hyperbolic 3-manifolds. Such 2-complexes are locally almost totally geodesic except along a…

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…

For oriented connected closed manifolds of the same dimension, there is a transitive relation: $M$ dominates $N$, or $M \ge N$, if there exists a continuous map of non-zero degree from $M$ onto $N$. Section 1 is a reminder on the notion of…

We prove that a closed arithmetic hyperbolic 3-manifold with positive first betti number has virtually infinite first betti number.

We prove that a representation from the fundamental group of a closed surface of negative Euler characteristic with values in the isometry group of a Riemannian manifold of sectional curvature bounded by -1 can be dominated by a Fuchsian…

Let N be a compact, orientable hyperbolic 3-manifold with connected, totally geodesic boundary of genus 2. If N has Heegaard genus at least 5, then its volume is greater than 6.89. The proof of this result uses the following dichotomy:…

We prove an extension of Milnor-Wood inequalities to a geometric situation. We study representations of the fundamental group of a compact manifold into the isometry group of a product of rank one spaces of the same dimension and show an…

Every closed orientable surface S has the following property: any two connected covers of S of the same degree are homeomorphic (as spaces). In this, paper we give a complete classification of compact 3-manifolds with empty or toroidal…

We provide two new proofs of a theorem of Cooper, Long and Reid which asserts that, apart from an explicit finite list of exceptional manifolds, any compact orientable irreducible 3-manifold with non-empty boundary has large fundamental…

We prove a finiteness result for the $\partial$-patterned guts decomposition of all 3-manifolds obtained by splitting a given orientable, irreducible and $\partial$-irreducible 3-manifold along a closed incompressible surface. Then using…

According to Mostow's celebrated rigidity theorem, the geometry of closed hyperbolic 3-manifolds is already determined by their topology. In particular, the volume of such manifolds is a topological invariant and, as such, has been…

Let M and N be n-dimensional connected orientable finite-volume hyperbolic manifolds with geodesic boundary, and let f be a given isomorphism between the fundamental groups of M and N. We study the problem whether there exists an isometry…

We construct for every connected surface $S$ of finite negative Euler characteristic and every $H \in [0,1)$, a hyperbolic 3-manifold $N(S,H)$ of finite volume and a proper, two-sided, totally umbilic embedding $f\colon S\to N(S,H)$ with…

We give a description of degree-one maps between closed, oriented 3-manifolds in terms of surgery. Namely, we show that there is a degree-one map from a closed, oriented 3-manifold $M$ to a closed, oriented 3-manifold $N$ if and only if $M$…