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The number of small covers over cubes

Suyoung Choi

Algebraic & Geometric Topology 8 (2008) 2391–2399
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.

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