Related papers: Complexity of 3-manifolds
One method for obtaining every closed orientable 3-manifold is as branched covering of the 3-sphere over a link. There is a classical topological result showing that the minimun possible number of sheets in the covering is three. In this…
In this short expository note, we give a detailed proof of Markov's theorem on the unsolvability of the homeomorphism problem and of the existence of unrecognizable manifolds in all dimensions larger than 3.
We give definitions of cohomology determinants for compact, connected, orientable 3-manifolds. We also give formulae relating cohomology determinants before and after gluing a solid torus along a torus boundary component. Cohomology…
An invariant of three-dimensional orientable manifolds is built on the base of a solution of pentagon equation expressed in terms of metric characteristics of Euclidean tetrahedra.
We define a new combinatorial class of triangulations of closed 3-manifolds, satisfying a weak version of 0-efficiency combined with a weak version of minimality, and study them using twisted squares. As an application, we obtain strong…
In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3--manifold, as well as a characterisation of manifolds realising our complexity bounds. As an application, we obtain the first…
We notice that a generic nonsingular gradient field $v = \nabla f$ on a compact 3-fold $X$ with boundary canonically generates a simple spine $K(f, v)$ of $X$. We study the transformations of $K(f, v)$ that are induced by deformations of…
Quantum invariants in low dimensional topology offer a wide variety of valuable invariants of knots and 3-manifolds, presented by explicit formulas that are readily computable. Their computational complexity has been actively studied and is…
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.
This article investigates the subject of rigid compact complex manifolds. First of all we investigate the different notions of rigidity (local rigidity, global rigidity, infinitesimal rigidity, etale rigidity and strong rigidity) and the…
A new class of 3-manifold invariants is constructed from representations of the category of framed tangles.
There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of $n$-fold coverings over orientable Euclidean manifolds…
This is the less official, English version of the proof of the fact that every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures.
This paper uses results on the classification of minimal triangulations of 3-manifolds to produce additional results, using covering spaces. Using previous work on minimal triangulations of lens spaces, it is shown that the lens space…
We give a description of finitely generated prosoluble subgroups of the profinite completion of $3$-manifold groups and virtually compact special groups.
We find the exact values of complexity for an infinite series of 3-manifolds. Namely, by calculating hyperbolic volumes, we show that c(N_n)=2n, where $c$ is the complexity of a 3-manifold and N_n is the total space of the punctured torus…
In this article we show that every closed orientable smooth $4$--manifold admits a smooth embedding in the complex projective $3$--space.
In this paper, we proved that any closed orientable 3-manifold 1-dominates at most finitely many geometric 3-manifolds.
A new lower bound on the complexity of a 3-manifold is given using the Z2-Thurston norm. This bound is shown to be sharp, and the minimal triangulations realising it are characterised using normal surfaces consisting entirely of…
We prove that fundamental groups of orientable (geometrizable) 3-manifolds have a solvable conjugacy problem.