The Number of Small Covers over Cubes
نویسنده
چکیده
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 Zn2 -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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تاریخ انتشار 2008