Some Centrally Symmetric Manifolds

Abstract

We show existence of centrally symmetric maps on surfaces all of whose faces are quadrangles and pentagons for each orientable genus $g\ge 0$. We also show existence of centrally symmetric maps on surfaces all of whose faces are hexagons for each orientable genus $g=2k-1$, $k\in \mathbb{N}$. We enumerate centrally symmetric triangulated manifolds of dimensions 2 and 3 with few vertices.

18 pages

References in corpus (2)

• A note on the existence of {k, k}-equivelar polyhedral maps
• Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres