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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 6

A note on small covers over cubes

Aslı Güçlükan İlhan
Sayfa
1997–2006
Yayın Tarihi
2022-10-18
DOI
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We also count the $\mathbb{Z}_2^n$-equivariant homeomorphism classes of orientable small covers and estimate the ratio between this number and the number of $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over an $n$-cube.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we obtain a bijection between the weakly $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over an $n$-cube and the orbits of the action of $\mathbb{Z}_2 \wr S_n$ on acyclic digraphs with $n$ vertices given by local complementation and reordering of vertices.
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Temel Bulgular & Veri:We obtain a similar formula for the number of orientable small covers over an $n$-cube.
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Sonuç & Katkı:We also count the $\mathbb{Z}_2^n$-equivariant homeomorphism classes of orientable small covers and estimate the ratio between this number and the number of $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over an $n$-cube.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:small cover · weakly equivariant homeomorphism · acyclic digraphs

Abstract

In this paper, we obtain a bijection between the weakly $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over an $n$-cube and the orbits of the action of $\mathbb{Z}_2 \wr S_n$ on acyclic digraphs with $n$ vertices given by local complementation and reordering of vertices. We obtain a similar formula for the number of orientable small covers over an $n$-cube. We also count the $\mathbb{Z}_2^n$-equivariant homeomorphism classes of orientable small covers and estimate the ratio between this number and the number of $\mathbb{Z}_2^n$-equivariant homeomorphism classes of small covers over an $n$-cube.

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Bu Makaleye Atıf Yap

İlhan, A. G. (2022). A note on small covers over cubes. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 6, 1997–2006. https://ajindex.com/articles/529670

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Kaynakça (13)

  1. A. Bouchet, Digraph decompositions and Eulerian systems, SIAM J. Algebraic Discrete Methods, 8, (3), 323-337, 1987
  2. M. Cai, X. Chen and Z. Lü, Small covers over prisms, Topol. Appl. 154, 2228–2234, 2007
  3. S. Choi, The number of small covers over cubes, Algebr. Geom. Topol. 8, 2391–2399, 2008
  4. S. Choi, The number of orientable small covers over cubes, Proc. Japan Acad. Ser. A, 86, 97–100, 2010
  5. S. Choi, M. Masuda and S. Oum, Classification of real Bott manifolds and acyclic digraphs, Trans. Amer. Math. Soc. 369, 2987–3011, 2017
  6. M.W. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus action, Duke Math. J. 62, 417–451, 1971
  7. D.G. Fon-Der-Flaass, Local complementations of simple and directed graphs, in: Discrete Analysis and Operations Research, 1, 15-34, 1996
  8. A. Garrison and R. Scott, Small covers over the dodecahedron and the 120-cell, Proc. Amer. Math. Soc. 131, 963–971, 2003
  9. Y. Kamishima and M. Masuda, Cohomological rigidity of real Bott manifolds, Algebr. Geom. Topol. 9, 2479-2502, 2009
  10. Z. Lü and M. Masuda, Equivariant classification of 2-torus manifolds, Colloq. Math. 115, 171–188, 2009
  11. M. Masuda, T.E. Panov, Semi-free circle actions, Bott towers, and quasitoric manifolds, Mat. Sb. 199, 95-122. 2008
  12. H. Nakayama and Y. Nishimura, The orientability of small covers and coloring simple polytopes, Osaka J. Math. 42, 243–256, 2005
  13. V.I. Rodinov, On the number of labeled acyclic digraphs, Discrete Math. 105, 319–321, 1992. [14] http://users.cecs.anu.edu.au/~bdm/data/digraphs.html.