Related papers: On embedding infinite cyclic covers in compact 3-m…

We prove that for any closed, connected, oriented 3-manifold M, there exists an infinite family of 2-fold branched covers of M that are hyperbolic 3-manifolds and surface bundles over the circle with arbitrarily large volume.

In this paper we study existence and lack thereof of closed embedded orientable co-dimension one totally geodesic submanifolds of minimal volume cusped orientable hyperbolic manifolds.

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…

For a noncompact 3-manifold with nonnegative Ricci curvature, we prove that either it is diffeomorphic to $\mathbb{R}^3$ or the universal cover splits. As a corollary, it confirms a conjecture of Milnor in dimension 3.

We consider homologically essential simple closed curves on Seifert surfaces of genus one knots in $S^3$, and in particular those that are unknotted or slice in $S^3$. We completely characterize all such curves for most twist knots: they…

Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with…

We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3-sphere, branched over two-bridge knots. Our method is to use the bi-twisted face-pairing constructions of Cannon, Floyd, and Parry;…

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…

E. Calabi and J. Cao showed that a closed geodesic of least length in a two-sphere with nonnegative curvature is always simple. Using min-max theory, we prove that for some higher dimensions, this result holds without assumptions on the…

We establish the real integral Hodge conjecture for 1-cycles on various classes of uniruled threefolds (conic bundles, Fano threefolds with no real point, some del Pezzo fibrations) and on conic bundles over higher-dimensional bases which…

We show that there are no smooth warped AdS$_3$ solutions in 10- and 11-dimensional supergravities which preserve strictly more than 16 supersymmetries and have internal space a compact without boundary manifold.

We show that the nonzero roots of the torsion polynomials associated to the infinite cyclic covers of a given compact, connected, orientable 3-manifold M are contained in a compact part of the complex plane a priori determined by M. This…

Let $K$ be a tame knot embedded in $\mathbf{S}^3$. We address the problem of finding the minimal degree non-cyclic cover $p:X \rightarrow \mathbf{S}^3 \smallsetminus K$. When $K$ has non-trivial Alexander polynomial we construct finite…

We prove that for any convex polygon $S$ with at least four sides, or a concave one with no parallel sides, and any $m>0$, there is an $m$-fold covering of the plane with homothetic copies of $S$ that cannot be decomposed into two…

The ends of a complete embedded minimal surface of {\em finite total curvature} are well understood (every such end is asymptotic to a catenoid or to a plane). We give a similar characterization for a large class of ends of {\em infinite…

For any alternating knot, it is known that the double branched cover of the $3$-sphere branched over the knot is an $L$-space. We show that the three-fold cyclic branched cover is also an $L$-space for any genus one alternating knot.

This article contains a proof of the fact that, under certain mild technical conditions, the action of the automorphism group of a cyclic 3-manifold cover of the type SxR, where S is a compact surface, yields a compact quotient. This result…

We consider irreducible 3-manifolds M that arise as knot complements in closed 3-manifolds and that contain at most two connected strict essential surfaces. The results in the paper relate the boundary slopes of the two surfaces to their…

This is the sequel to our first paper concerning the balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. We prove the uniqueness of such an embedding. The proof relies on fine estimates of the…

This paper gives a proof that the universal cover of a closed 3-manifold built from three $\pi_1$-injective handlebodies is homeomorphic to $\mathbb R^3$. This construction is an extension to handlebodies of the conditions for gluing of…