Homology, Homotopy and Applications

Volume 13 (2011)

Number 1

Generalized Davis-Januszkiewicz spaces, multicomplexes and monomial rings

Pages: 205 – 221

DOI: http://dx.doi.org/10.4310/HHA.2011.v13.n1.a8

Author

Alvise J. Trevisan (Faculteit der ExacteWetenschappen, VU University Amsterdam, The Netherlands)

Abstract

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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