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

Small covers over products of a polygon with a simplex

Yanchang CHEN
Yanying WANG
Pages
161–172
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, we calculate the number of equivariant homeomorphism classes of all orientable small covers over the product.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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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Key Findings & Data: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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Conclusion & Impact:Moreover, we calculate the number of equivariant homeomorphism classes of all orientable small covers over the product.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Small cover · equivariant homeomorphism · polytope

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.

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.

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Cite This Article

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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References (6)

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  3. Choi, S.: The number of orientable small covers over cubes. Proc. Japan Acad. Ser. A. 86, 97–100 (2010).
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  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]