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Dergiler / Turkish Journal of Mathematics / 2012 / Cilt: 36 - Sayı: 1

Small covers over products of a polygon with a simplex

Yanchang CHEN
Yanying WANG
Sayfa
161–172
Yayın Tarihi
2022-11-05
DOI
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Moreover, we calculate the number of equivariant homeomorphism classes of all orientable small covers over the product.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:Moreover, we calculate the number of equivariant homeomorphism classes of all orientable small covers over the product.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Small cover · equivariant homeomorphism · polytope

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.

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Bu Makaleye Atıf Yap

CHEN, Y., WANG, Y. (2022). Small covers over products of a polygon with a simplex. Turkish Journal of Mathematics, Cilt: 36 - Sayı: 1, 161–172. https://ajindex.com/articles/608406

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Kaynakça (6)

  1. Cai, M., Chen, X., L¨u, Z.: Small covers over prisms. Topology and its Applications. 154, 2228–2234 (2007).
  2. Choi, S.: The number of small covers over cubes. Algebr. Geom. Topol. 8, 2391–2399 (2008).
  3. Choi, S.: The number of orientable small covers over cubes. Proc. Japan Acad. Ser. A. 86, 97–100 (2010).
  4. Davis, M., Januszkiewicz, T.: Convex polytopes, Coxeter orbifolds and torus actions. Duke Math J. 62, 417–451 (1991). L¨u, Z., Masuda, M.: Equivariant classiŞcation of 2-torus manifolds. Colloq. Math. 115, 171–188 (2009).
  5. Nakayama, H., Nishimura, Y.: The orientability of small covers and coloring simple polytopes. Osaka J. Math. 42, –256 (2005).
  6. Ziegler, G. M.: Lectures on Polytopes, Graduate Texts in Math., Berlin, Springer-Verlag, 1994. Yanying WANG and Yanchang CHEN College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, P. R. CHINA e-mail: [email protected], [email protected]