Algebraic & Geometric Topology

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 formulas of the number of small covers over an n–cube (generally, a product of simplices) up to Davis–Januszkiewicz equivalence classes and 2n–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
Received: 3 October 2008
Revised: 4 November 2008
Accepted: 13 November 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 37F20: Combinatorics and topology 57S10: Compact groups of homeomorphisms
Secondary: 57N99: None of the above, but in this section

Keywords
small cover acyclic digraph real torus action equivariant homeomorphism weak equivariant homeomorphism

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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