Geodesic
The number of small covers over cubes
Choi, Suyoung1
1KAIST, Department of Mathematical Sciences, 335 Gwahangno, Yuseong-gu, Daejeon, 305-701, South Korea
Algebraic and Geometric Topology, Tome 8 (2008) no. 4, pp. 2391-2399
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In the present paper we find a bijection between the set of small covers over an n–cube and the set of acyclic digraphs with n labeled nodes. Using this, we give formulas of the number of small covers over an n–cube (generally, a product of simplices) up to Davis–Januszkiewicz equivalence classes and ℤ2n–equivariant homeomorphism classes. Moreover we prove that the number of acyclic digraphs with n unlabeled nodes is an upper bound of the number of small covers over an n–cube up to homeomorphism.

DOI : 10.2140/agt.2008.8.2391
Keywords: small cover, acyclic digraph, real torus action, equivariant homeomorphism, weak equivariant homeomorphism

Choi, Suyoung  1

1 KAIST, Department of Mathematical Sciences, 335 Gwahangno, Yuseong-gu, Daejeon, 305-701, South Korea 
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Choi, Suyoung. The number of small covers over cubes. Algebraic and Geometric Topology, Tome 8 (2008) no. 4, pp. 2391-2399. doi: 10.2140/agt.2008.8.2391

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