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arXiv · 0802.1982

The number of small covers over cubes

Suyoung Choi
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Abstract

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 a formula of the number of small covers over an $n$-cube (generally, a product of simplices) up to Davis-Januszkiewicz equivalence classes and $\mathbf{Z}^n$-equivariant diffeomorphism 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 diffeomorphism.

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Suyoung Choi. 2008-03-04. The number of small covers over cubes. https://doi.org/10.2140/agt.2008.8.2391

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