Dergiler / Turkish Journal of Mathematics / 2012 / Cilt: 36 - Sayı: 1
Small covers over products of a polygon with a simplex
- Sayfa
- 161–172
- DOI
- —
Özet
The equivariant homeomorphism class of an (orientable) small cover over a simple convex polytope Pn bijectively corresponds to the equivalence class of its (orientable) coloring under the action of automorphism group of face poset of Pn. By calculating the number of orbits of group actions we determine the number of equivariant homeomorphism classes of small covers over products of a polygon with a simplex. Moreover, we calculate the number of equivariant homeomorphism classes of all orientable small covers over the product.
Abstract
The equivariant homeomorphism class of an (orientable) small cover over a simple convex polytope Pn bijectively corresponds to the equivalence class of its (orientable) coloring under the action of automorphism group of face poset of Pn. By calculating the number of orbits of group actions we determine the number of equivariant homeomorphism classes of small covers over products of a polygon with a simplex. Moreover, we calculate the number of equivariant homeomorphism classes of all orientable small covers over the product.