相关论文: Spines of 3-Manifolds as Polyhedra with Identified…

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in…

We consider a family of cyclic presentations and show that, subject to certain conditions on the defining parameters, they are spines of closed 3-manifolds. These are new examples where the reduced Whitehead graphs are of the same type as…

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…

In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3-manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed,…

We classify all closed non-orientable $\mathbb{P}^2$-irreducible 3-manifolds obtained by identifying the faces of a cube. These turn out to be the closed non-orientable $\mathbb{P}^2$-irreducible 3-manifolds with surface-complexity one. We…

It is well known that every compact oriented 3-manifold admits an ideal triangulation, and that any two such triangulations with at least two ideal tetrahedra are related by a sequence of Pachner $2$-$3$ moves. Motivated by constructions in…

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.

$2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed branch curves. We obtain a list of all closed $3$-manifolds that have a $2$-stratifold as a spine.

We analyze polyhedra composed of hexagons and triangles with three faces around each vertex, and their 3-regular planar graphs of edges and vertices, which we call "trihexes". Trihexes are analogous to fullerenes, which are 3-regular planar…

The problem of classifying, upto isometry (or similarity), the orientable spherical, Euclidean and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. In the…

We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer…

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.

An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the…

After surveying existing proofs that every closed, orientable 3-manifold is parallelizable, we give three proofs using minimal background. In particular, our proofs use neither spin structures nor the theory of Stiefel-Whitney classes.

We give a new elementary proof of the parallelizability of closed orientable 3-manifolds. We use as the main tool the fact that any such manifold admits a Heegaard splitting.

A new formula is obtained in algebraic topology, in terms of Betti numbers, and a new method, called the spinal method, is suggested and developed for generating quadrangulations of closed orientable surfaces. Those surfaces arise as the…

In this short note we show that the closed cone of moving curves of a smooth Fano-threefold is polyhedral. The proof relies on a famous result of Bucksom, Demailly, Paun and Peternell which says that the strongly movable cone is dual to the…

The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed…

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…

Two single parameter families of polyhedra $P(\psi)$ are constructed in three dimensional spaces of constant curvature $C(\psi)$. Identification of the faces of the polyhedra via isometries results in cone manifolds $M(\psi)$ which are…