相关论文: Any 3-manifold 1-dominates at most finitely many g…

For a closed orientable irreducible $3$-manifold $M$ that admits a co-orientable taut foliation with one-sided branching, we show that $\pi_1(M)$ is left orderable.

We describe an algorithm which has enabled us to give a complete list, without repetitions, of all closed oriented irreducible 3-manifolds of complexity up to 9. More interestingly, we have actually been able to give a "name" to each such…

In this article we show that every closed orientable smooth $4$--manifold admits a smooth embedding in the complex projective $3$--space.

The goal of the paper is to give characterization of closed connected manifolds which admit a global multisympletic 3-form of some algebraic type. A generic type of such 3-form is equivalent to a G2-structure. This is the most interesting…

We prove that a complete hyperbolic 3-manifold of finite volume does not admit a properly embedded noncompact surface of finite topology with constant mean curvature greater than or equal to 1.

We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for…

A random group contains many subgroups which are isomorphic to the fundamental group of a compact hyperbolic 3-manifold with totally geodesic boundary. These subgroups can be taken to be quasi-isometrically embedded. This is true both in…

We prove Calegari's conjecture that every quasigeodesic flow on a closed hyperbolic 3-manifold has closed orbits.

We provide a proof that the classes of finitely generated Kleinian groups and of three-manifold groups are quasi-isometrically rigid.

Manifolds all of whose geodesics are closed have been studied a lot, but there are only few examples known. The situation is different if one allows in addition for orbifold singularities. We show, nevertheless, that the abundance of new…

In this paper we explore the topological properties of self-replicating, 3-dimensional manifolds, which are modeled by idempotents in the (2+1)-cobordism category. We give a classification theorem for all such idempotents. Additionally, we…

We introduce the notion of a manifold admitting a simple compact Cartan 3-form $\om^3$. We study algebraic types of such manifolds specializing on those having skew-symmetric torsion, or those associated with a closed or coclosed 3-form…

In this paper we show that a given set of lengths of closed geodesics, there are only finitely many convex cocompact hyperbolic 3-manifolds with that specified length spectrum, homotopy equivalent to a given 3-manifold without a handlebody…

We prove that there is an algorithm which determines whether or not a given 2-polyhedron can be embedded into some integral homology 3-sphere. This is a corollary of the following main result. Let $M$ be a compact connected orientable…

We study transversely Lorentzian foliations on the closed 3-manifolds. We classify them under a completeness hypothesis and we deduce the dual classification of codimension 1 geodesically complete timelike totally geodesic foliations.…

The paper contains a new proof that a complete, non-compact hyperbolic $3$-manifold $M$ with finite volume contains an immersed, closed, quasi-Fuchsian surface.

We present a sketch of the proof of the following theorems: (1) Every 3-manifold has only finitely many homotopy classes of 2-plane fields which carry tight contact structures. (2) Every closed atoroidal 3-manifold carries finitely many…

We prove that orientable index one minimal surfaces in spherical space forms with large fundamental group have genus at most two. This confirms a conjecture of R. Schoen for an infinite class of 3-manifolds.

We show that, if a rational homology 3-sphere $Y$ bounds a positive definite smooth 4-manifold, then there are finitely many negative definite lattices, up to the stable-equivalence, which can be realized as the intersection form of a…

This note surveys recent progress toward the profinite rigidity of orientable finite-volume hyperbolic 3-manifolds. Beginning in a brief review of some basic settings of profinite completion and rigidity of general groups, we state the…