The number of small covers over cubes

Choi, Suyoung

doi:10.2140/agt.2008.8.2391

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The number of small covers over cubes

Suyoung Choi

Algebraic & Geometric Topology 8 (2008) 2391–2399

DOI: 10.2140/agt.2008.8.2391

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 $ℤ_{2}^{n}$ –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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 37F20, 57S10

Secondary: 57N99

References

Publication

Received: 3 October 2008

Revised: 4 November 2008

Accepted: 13 November 2008

Published: 20 December 2008

Authors

Suyoung Choi
KAIST Department of Mathematical Sciences 335 Gwahangno, Yuseong-gu Daejeon, 305-701 South Korea
http://topology.kaist.ac.kr/schoi

Volume 8, issue 4 (2008)