Related papers: Open 3-manifolds which are connected sums of close…

The classical Kneser-Milnor theorem says that every closed oriented connected 3-dimensional manifold admits a unique connected sum decomposition into manifolds that cannot be decomposed any further. We discuss to what degree such…

In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is…

After a short summary of known results on surface-complexity of closed 3-manifolds, we will classify all closed orientable 3-manifolds with surface-complexity one.

In this paper, we describe geometrical constructions to obtain triangulations of connected sums of closed orientable triangulated 3-manifolds. Using these constructions, we show that it takes time polynomial in the number of tetrahedra to…

It has been shown by V. Colin that every tight contact 3-manifold can be written as a connected sum of prime manifolds. Here we prove that the summands in this decomposition are unique up to order and contactomorphism.

We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils…

We extend Matveev's theory of complexity for 3-manifolds, based on simple spines, to (closed, orientable, locally orientable) 3-orbifolds. We prove naturality and finiteness for irreducible 3-orbifolds, and, with certain restrictions and…

We give several criteria on a closed, oriented 3-manifold that will imply that it is the boundary of a (simply connected) 4-manifold that admits infinitely many distinct smooth structures. We also show that any weakly fillable contact…

This paper concerns the class of contractible open 3-manifolds which are ``locally finite strong end sums'' of eventually end-irreducible Whitehead manifolds. It is shown that whenever a 3-manifold in this class is a covering space of…

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…

Let $M$ be a $3$-manifold with connected non-vacuos boundary which is not spherical. Assume that $N$ is another $3$-manifold with vacuous boundary and $N^{\ast}$ is the $3$-manifold obtained by removing from $N$ the interior of a $3$-cell.…

Let C be some class of objects equipped with a set of simplifying moves. When we apply these to a given object M in C as long as possible, we get a root of M. Our main result is that under certain conditions the root of any object exists…

In this paper we develop the theory of finite-type invariants for homologically nontrivial 3-manifolds. We construct an infinite-dimensional affine space with a hypersurface in it corresponding to manifolds with Morse singularities.…

This paper adresses the following problem: Given a closed orientable three-manifold M, are there at most finitely many closed orientable three-manifolds 1-dominated by M? We solve this question for the class of closed orientable graph…

An end sum is a non-compact analogue of a connected sum. Suppose we are given two connected, oriented $n$-manifolds $M_1$ and $M_2$. Recall that to form their connected sum one chooses an $n$-ball in each $M_i$, removes its interior, and…

We study connected sum at infinity on smooth, open manifolds. This operation requires a choice of proper ray in each manifold summand. In favorable circumstances, the connected sum at infinity operation is independent of ray choices. For…

In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a semisimple Lie algebra, or by a semisimple…

We classify the $3$-manifolds obtained as the preimages of arcs on the plane for simplified $(2, 0)$-trisection maps, which we call vertical $3$-manifolds. Such a $3$-manifold is a connected sum of a $6$-tuple of vertical $3$-manifolds over…

A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for…

We establish a correspondence between trisections of smooth, compact, oriented $4$--manifolds with connected boundary and diagrams describing these trisected $4$--manifolds. Such a diagram comes in the form of a compact, oriented surface…