相关论文: 3-manifolds built from injective handlebodies

In the paper we introduce the construction of invariants for 3-manifolds, based on the same key concepts as the classical Dijkgraaf-Witten invariant. We introduce the notion of a special $G$-system and describe how each system induces the…

In the curve complex for a surface, a handlebody set is the set of loops that bound properly embedded disks in a given handlebody bounded by the surface. A boundary set is the set of non-separating loops in the curve complex that bound…

Harer, Kas and Kirby have conjectured that every handle decomposition of the elliptic surface $E(1)_{2,3}$ requires both 1- and 3-handles. In this article, we construct a smooth 4-manifold which has the same Seiberg-Witten invariant as…

We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the…

This paper gives necessary and sufficient conditions on a compact, connected, orientable 3-manifold M for it to contain a knot K such that M-K is irreducible and pi_1(M) embeds in pi_1(M-K). This result provides counterexamples to a…

In this paper, we consider decompositions of closed orientable 3-manifolds with more than 3 handlebodies, where the union of intersections of handlebodies is a multibranched surface. We define stabilization operations for such…

Suppose that M is a fibered three-manifold whose fiber is a surface of positive genus with one boundary component. Assume that M is not a semi-bundle. We show that infinitely many fillings of M along dM are virtually Haken. It follows that…

Using contact surgery we define families of contact structures on certain Seifert fibered three-manifolds. We prove that all these contact structures are tight using contact Ozsath-Szabo invariants. We use these examples to show that, given…

We prove that fundamental groups of non-orientable 3-manifolds have a solvable conjugacy problem, and construct an algorithm. Together with our earlier work on the conjugacy problem in groups on orientable geometrizable 3-manifolds, all…

We establish a canonical gluing procedure for Seiberg-Witten monopoles on the two pieces of a closed, oriented 4-manifold X which is split along a 3-dimensional closed, oriented submanifold. We only assume that the (unperturbed) character…

Haken showed that the Heegaard splittings of reducible 3-manifolds are reducible, that is, a reducing 2-sphere can be found which intersects the Heegaard surface in a single simple closed curve. When the genus of the "interesting" surface…

Non-isotopic Heegaard splittings of non-minimal genus were known previously only for very special 3-manifolds. We show in this paper that they are in fact a wide spread phenomenon in 3-manifold theory: We exhibit a large class of knots and…

There has been much recent interest into those properties of a 3-manifold determined by the profinite completion of its fundamental group. In this paper we give readily computable criteria specifying precisely when two orientable graph…

The aim of this article is to introduce and study certain topological invariants for closed, oriented three-manifolds Y. These groups are relatively Z-graded Abelian groups associated to SpinC structures over Y. Given a genus g Heegaard…

It is shown that a hyperbolic knot in the 3-sphere admits at most nine integral surgeries yielding 3-manifolds which are reducible or whose fundamental groups are not infinite word-hyperbolic.

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…

We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many…

If a 3--manifold $Y$ contains a non-separating sphere, then some twisted Heegaard Floer homology of $Y$ is zero. This simple fact allows us to prove several results about Dehn surgery on knots in such manifolds. Similar results have been…

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 define for each g>=2 and k>=0 a set M_{g,k} of orientable hyperbolic 3-manifolds with $k$ toric cusps and a connected totally geodesic boundary of genus g. Manifolds in M_{g,k} have Matveev complexity g+k and Heegaard genus g+1, and…