Homology, Homotopy and Applications

Volume 15 (2013)

Number 2

The geometric realization of monomial ideal rings and a theorem of Trevisan

Pages: 1 – 7

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n2.a1


A. Bahri (Department of Mathematics, Rider University, Lawrenceville, New Jersey, U.S.A.)

M. Bendersky (Department of Mathematics, Hunter College, New York City)

F. R. Cohen (Department of Mathematics, University of Rochester, New York, U.S.A.)

S. Gitler (El Colegio Nacional, Centro Historico, Mexico City, Mexico)


A direct proof is presented of a form of Alvise Trevisan’s theorem that every monomial ideal ring is represented by the cohomology of a topological space. Certain of these rings are shown to be realized by polyhedral products indexed by simplicial complexes.


monomial ideal ring, Stanley-Reisner ring, Davis-Januszkiewicz space, polar-ization, polyhedral product

2010 Mathematics Subject Classification

Primary 13F55. Secondary 55T20, 57T35.

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Published 4 December 2014