Decomposition theorems for the torus, projective plane and Klein bottle (Q1108282)

A map is called polyhedral if every (closed) face is a cell and if no two faces have a multiply connected union. The author shows that every polyhedral map on the torus is the union of two face-disjoint subcomplexes that are annuli. Similar decomposition theorems are proved for the Klein bottle and projective plane. As a corollary it is proved that the polyhedral maps on these surfaces are isomorphic to maps obtained by identifying boundary complexes of 3-polytopes. Finally, it is shown that each 5-connected toroidal triangulation has a Hamiltonian path.