Related papers: Layered models for closed 3-manifolds
We apply the local removable singularity theorem for minimal laminations and the local picture theorem on the scale of topology to obtain two descriptive results for certain possibly singular minimal laminations of $\mathbb{R}^3$. These two…
A (complete) matching of the cells of a triangulated manifold can be thought as a combinatorial or discrete version of a nonsingular vector field. We give several methods for constructing such matchings.
We study in detail the closed flat Riemannian 3-manifolds.
We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…
Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. Except few, all the known…
Gabai showed that the Whitehead manifold is the union of two submanifolds each of which is homeomorphic to $\mathbb R^3$ and whose intersection is again homeomorphic to $\mathbb R^3$. Using a family of generalizations of the Whitehead Link,…
In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…
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…
The existence of essential closed surfaces surfaces is proven for finite coverings of 3-manifolds that are triangulated by finitely many topological ideal tetrahedra and admit a regular, negatively curved, ideal structure.
A celebrated result concerning triangulations of a given closed 3-manifold is that any two triangulations with the same number of vertices are connected by a sequence of so-called 2-3 and 3-2 moves. A similar result is known for ideal…
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…
We extend Turaev's theory of Euler structures and torsion invariants on 3-manifolds to the case of vector fields having generic behavior on the boundary. This allows to easily define gluings of Euler structures and to develop a completely…
Given a complex structure, we investigate diverging sequences of projective structures on the fixed complex structure in terms of Thurston's parametrization. In particular, we will give a geometric proof to the theorem by Kapovich stating…
Given an orientable ideally triangulated $3$--manifold $M$, we define a system of real valued equations and inequalities whose solutions can be used to construct projective structures on $M$. These equations represent a unifying framework…
We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted…
On a geometrical view, the conception of map geometries are introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surface. Results convinced one that map geometries are…
We prove combination theorems in the spirit of Klein and Maskit in the context of discrete convergence groups acting geometrically finitely on their limit sets. As special cases, we obtain combination theorems for geometrically finite…
We give a new definition of a universal finite type invariant of three-dimensional oriented rational homology spheres which counts configurations of trivalent graphs in such manifolds. Kontsevich introduced this invariant following Witten's…
The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.
In this paper we explore the topological properties of self-replicating, 3-dimensional manifolds, which are modeled by idempotents in the (2+1)-cobordism category. We give a classification theorem for all such idempotents. Additionally, we…