## Algebraic & Geometric Topology

### The number of small covers over cubes

Suyoung Choi

#### 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 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 8, Number 4 (2008), 2391-2399.

Dates
Revised: 4 November 2008
Accepted: 13 November 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796938

Digital Object Identifier
doi:10.2140/agt.2008.8.2391

Mathematical Reviews number (MathSciNet)
MR2465745

Zentralblatt MATH identifier
1160.37368

#### Citation

Choi, Suyoung. The number of small covers over cubes. Algebr. Geom. Topol. 8 (2008), no. 4, 2391--2399. doi:10.2140/agt.2008.8.2391. https://projecteuclid.org/euclid.agt/1513796938

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