相关论文: Hyperbolic rational homology spheres not admitting…

We characterize when some small Seifert fibered spaces can be the convex boundaries of symplectic rational homology balls and give strong restrictions for others to bound such manifolds. In particular, we show that the only spherical…

We analyse the existence question for essential laminations in 3-manifolds. The purpose is to prove that there are infinitely many closed hyperbolic 3-manifolds which do not admit essential laminations. This answers in the negative a…

It is an important question whether it is possible to put a geometry on a given manifold or not. It is well known that any simply connected closed manifold admitting a real projective structure must be a sphere. Therefore, any simply…

In this paper we construct an infinite family of homotopically rigid spaces. These examples are then used as building blocks to forge highly connected rational spaces with prescribed finite group of self-homotopy equivalences. They are also…

In this paper we study the groups of contactomorphisms of a closed contact manifold from a topological viewpoint. First we construct examples of contact forms on spheres whose Reeb flow has a dense orbit. Then we show that the unitary group…

Auckly gave two examples of irreducible integer homology spheres (one toroidal and one hyperbolic) which are not surgery on a knot in the three-sphere. Using Heegaard Floer homology, the authors and Karakurt provided infinitely many small…

We prove that, for any two finite volume hyperbolic $3$-manifolds, the amalgamation of their fundamental groups along any nontrivial geometrically finite subgroup is not LERF. This generalizes the author's previous work on nonLERFness of…

Let $\Sigma$ be a simply connected rational homology sphere. A pair of disjoint closed submanifolds $M_+, M_-$ in $\Sigma$ are called dual to each other if the complement $\Sigma - M_+$ strongly homotopy retracts onto $M_-$ or vice-versa.…

We prove the non--triviality of the Reeb flow for the (2n+1)--dimensional standard contact spheres inside the fundamental group of their contactomorphism group, n greater than 3. The argument uses the existence of homotopically non--trivial…

The space of orientation-compatible almost complex structures on the six-dimensional sphere naturally contains a copy of seven-dimensional real projective space. We show that the inclusion induces an isomorphism on fundamental groups and…

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost…

In the present paper, we construct a cusped hyperbolic $4$-manifold with all cusp sections homeomorphic to the Hantzsche-Wendt manifold, which is a rational homology sphere. By a result of Gol\'enia and Moroianu, the Laplacian on $2$-forms…

In this work, we prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application of our main result, we provide several new examples of manifolds which admit taut contact…

In this paper, we study contact structures on any open 3-manifold V which is the interior of a compact 3-manifold. To do this, we introduce proper contact isotopy invariants called the slope at infinity and the division number at infinity.…

In this paper we consider a large family of graphs of hierarchically hyperbolic groups (HHG) and show that their fundamental groups admit HHG structures. To do that, we will investigate the notion of hierarchical quasi convexity and show…

We classify tight contact structures on the small Seifert fibered 3--manifold M(-1; r_1, r_2, r_3) with r_i in (0,1) and r_1, r_2 \geq 1/2. The result is obtained by combining convex surface theory with computations of contact…

We present new explicit tight and overtwisted contact structures on the (round) 3-sphere and the (flat) 3-torus for which the ambient metric is weakly compatible. Our proofs are based on the construction of nonvanishing curl eigenfields…

We consider strong symplectic fillings of the unit cotangent bundle of a hyperbolic surface, equipped with its canonical contact structure. We show that every finitely presentable group can be realised as the fundamental group of such a…

We construct an infinite family of odd-symplectic forms (also known as Hamiltonian structures) on the 3-sphere that do not admit a symplectic cobordism to the standard contact structure on the 3-sphere. This answers in the negative a…

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…