Thick triangulations of hyperbolicn-manifolds

Triangulations of Manifolds

In topology, a basic building block for spaces is the n-simplex. A 0-simplex is a point, a 1-simplex is a closed interval, a 2-simplex is a triangle, and a 3-simplex is a tetrahedron. In general, an n-simplex is the convex hull of n + 1 vertices in n-dimensional space. One constructs more complicated spaces by gluing together several simplices along their faces, and a space constructed in this ...

Layered - Triangulations of 3 – Manifolds

A family of one-vertex triangulations of the genus-g-handlebody, called layered-triangulations, is defined. These triangulations induce a one-vertex triangulation on the boundary of the handlebody, a genus g surface. Conversely, any one-vertex triangulation of a genus g surface can be placed on the boundary of the genus-g-handlebody in infinitely many distinct ways; it is shown that any of thes...

Minimal Triangulations of 3 - manifolds

Triangulations of Seifert Fibred Manifolds

It is not completely unreasonable to expect that a computable function bounding the number of Pachner moves needed to change any triangulation of a given 3-manifold into any other triangulation of the same 3-manifold exists. In this paper we describe a procedure yielding an explicit formula for such a function if the 3-manifold in question is a Seifert fibred

Classification of Simplicial Triangulations of Topological Manifolds

In this note we announce theorems which classify simplicial (not necessarily combinatorial) triangulations of a given topological «-manifold M, n > 7 (> 6 if dM = 0 ) , in terms of homotopy classes of lifts of the classifying map r: M —• BTOP for the stable topological tangent bundle of M to a classifying space BTRIn which we introduce below. The (homotopic) fiber of the natural map ƒ: BTRIn —•...