Related papers: An algorithm to detect laminar 3-manifolds

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…

We present a practical algorithm to test whether a 3-manifold given by a triangulation or an ideal triangulation contains a closed essential surface. This property has important theoretical and algorithmic consequences. As a testament to…

We define essential and strongly essential triangulations of 3-manifolds, and give four constructions using different tools (Heegaard splittings, hierarchies of Haken 3-manifolds, Epstein-Penner decompositions, and cut loci of Riemannian…

We describe theoretical backgrounds for a computer program that recognizes all closed orientable 3-manifolds up to complexity 8. The program can treat also not necessarily closed 3-manifolds of bigger complexities, but here some…

We prove the existence of a new algorithm for 3-sphere recognition based on Groebner basis methods applied to the variety of $\text{\em SL}(2,\C)$-representation of the fundamental group. An essential input is a recent result of the second…

We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after…

In this paper, we give a new simplified calculation of the Lusternik-Schnirelmann category of closed 3-manifolds. We also describe when 3-manifolds have detecting elements and prove that 3-manifolds satisfy the equality of the Ganea…

In the paper we prove that every closed orientable three-manifold admits a parabolic foliation.

We present a fast enumeration algorithm for combinatorial 2- and 3-manifolds. In particular, we enumerate all triangulated surfaces with 11 and 12 vertices and all triangulated 3-manifolds with 11 vertices. We further determine all…

This article presents a survey on the topic of embedding 3-manifolds in definite 4-manifolds, emphasizing the latest progress in the field. We will focus on the significant role played by Donaldson's diagonalization theorem and the…

This is a problem list in the theory of foliations and laminations of 3-manifolds. The focus is on the relationship of foliations and laminations with other aspects of 3-manifold topology, especially with the Thurston theory of geometric…

We construct 3-manifolds which have at least two inequivalent embeddings such that both complementary regions have abelian fundamental group.

We give an algorithm to find vertical essential tori in small Seifert fiber spaces with infinite fundamental groups. This implies that there are algorithms to decide whether a 3-manifold is a Seifert fiber space.

We present an algorithm aimed to recognize if a given tensor is a non-identifiable rank-3 tensor.

We propose an effective algorithm that enumerates (and actually finds) all 3-edge colorings and Hamiltonian cycles in a cubic graph. The idea is to make a preliminary run that separates the vertices into two types: ``rigid'' (such that the…

We show that every topological surface lamination of a 3-manifold M is isotopic to one with smoothly immersed leaves. This carries out a project proposed by Gabai in [Problems in foliations and laminations, AMS/IP Stud. Adv. Math. 2.2…

If M is a manifold with compressible boundary, we analyze essential disks in M, as well as incompressible, but not necessarily boundary incompressible, surfaces in M. We are most interested in the case where M is a handlebody or compression…

We outline a rigorous algorithm, first suggested by Casson, for determining whether a closed orientable 3-manifold M is hyperbolic, and to compute the hyperbolic structure, if one exists. The algorithm requires that a procedure has been…

There are many fundamental algorithmic problems on triangulated 3-manifolds whose complexities are unknown. Here we study the problem of finding a taut angle structure on a 3-manifold triangulation, whose existence has implications for both…

Adyan and Rabin showed that most properties of groups cannot be algorithmically recognized from a finite presentation alone. We prove that, if one is also given a solution to the word problem, then the class of fundamental groups of closed,…