Abstract (EN):
We provide a multiple purpose algorithm for generating oriented matroids. An application disproves a conjecture of Grunbaum that every closed triangulated orientable 2-manifold can be embedded geometrically in R-3, i.e., with flat triangles and without self-intersections. We can show in particular that there exists an infinite class of orientable triangulated closed 2-manifolds for each genus g greater than or equal to 6 that cannot be embedded geometrically in Euclidean 3-space. Our algorithm is interesting in its own right as a tool for many investigations in which oriented matroids play a key role.
Language:
English
Type (Professor's evaluation):
Scientific
No. of pages:
12