𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On a triangulation of the 3-ball and the solid torus

✍ Scribed by Ge´za Bohus; William Jockusch; Carl W. Lee; Nagabhushana Prabhu


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
302 KB
Volume
187
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis


We show that neither the 3-ball nor the solid torus admits a triangulation in which (i) every vertex is on the boundary, and (ii) every tetrahedron has exactly one triangle on the boundary. Such triangulations are relevant to an unresolved conjecture of Perles.


📜 SIMILAR VOLUMES


Generating the 4-connected and strongly
✍ D.W. Barnette 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 978 KB

The triangulations of the torus can be generated from a set of 21 minimal triangulations by vertex splitting. We show that if we never create a 3-valent vertex when we split them we generate the 4-connected triangulations. In addition if we never create two adjacent 4-valent vertexes then we gener

A Simple Proof of an Estimate for the Ap
✍ Piotr Mankiewicz; Carsten Schütt 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 125 KB

We give a simple proof of an estimate for the approximation of the Euclidean ball by a polytope with a given number of vertices with respect to the volume of the symmetric difference metric and relatively precise estimate for the Delone triangulation numbers. We also study the same problem for a giv

Global analytic, Gevrey and C∞ hypoellip
✍ A. Alexandrou Himonas; Gerson Petronilho; L. A. Carvalho dos Santos 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 223 KB

## Abstract It is proved that a class of sub‐Laplacians on the 3‐dimensional torus is globally analytic, Gevrey and __C__^∞^ hypoelliptic if and only if either a Diophantine condition holds or there is a point of finite type for the vector fields defining the operator under consideration. This work

Graphs on the Torus and Geometry of Numb
✍ A. Schrijver 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 424 KB

We show that if \(G\) is a graph embedded on the torus \(S\) and each nonnullhomotopic closed curve on \(S\) intersects \(G\) at least \(r\) times, then \(G\) contains at least \(\left\lfloor\frac{3}{4} r\right\rfloor\) pairwise disjoint nonnullhomotopic circuits. The factor \(\frac{3}{4}\) is best

On the Interval Number of a Triangulated
✍ Thomas Andreae 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 414 KB 👁 2 views

The interval number of a simple undirected graph G, denoted i(G), is the least nonnegative integer r for which we can assign to each vertex in G a collection of at most r intervals on the real line such that two distinct vertices u and w of G are adjacent if and only if some interval for u intersect