Homology, Homotopy and Applications
Volume 13 (2011)
Generalized Davis-Januszkiewicz spaces, multicomplexes and monomial rings
Pages: 205 – 221
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.
Davis-Januszkiewicz space; monomial ring; Stanley-Rainer ring; simplicial complex; polarization; homotopy fiber
2010 Mathematics Subject Classification
13F55, 55Pxx, 55U05