Generalized Davis-Januszkiewicz spaces, multicomplexes and monomial rings

We show that every monomial ring can be realized topologically by a certain topological space. This space is called a generalized Davis-Januszkiewicz space and can be thought of as a colimit over a multicomplex, a combinatorial object generalizing a simplicial complex. Furthermore, we show that such a space is obtained as the homotopy fiber of a certain map with total space the classical Davis-Januszkiewicz space.

Keywords

Davis-Januszkiewicz space, monomial ring, Stanley-Rainer ring, simplicial complex, polarization, homotopy fiber

2010 Mathematics Subject Classification

13F55, 55Pxx, 55U05

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Published 12 July 2011