On polyhedral product spaces over polyhedral joins

Elizabeth Vidaurre

doi:10.4310/HHA.2018.v20.n2.a13

On polyhedral product spaces over polyhedral joins

Elizabeth Vidaurre

Mathematics and Computer Studies

Research & Scholarship: Contribution to journal › Article › peer-review

Abstract

The construction of a simplicial complex given by polyhedral joins (introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen and Gitler’s � -construction and simplicial wedge construction. This article gives a cohomological decomposition of a polyhedral product over a polyhedral join. A formula for the Hilbert–Poincaré series is given, which generalizes Ayzenberg’s formula for the moment-angle complex.

Original language	American English
Journal	Homology, Homotopy and Applications
Volume	20
DOIs	https://doi.org/10.4310/HHA.2018.v20.n2.a13
State	Published - Jun 2018

Keywords

cohomology ring
moment-angle complex
simplicial complex
Stanley–Reisner ring
simplicial wedge construction

Disciplines

Physical Sciences and Mathematics

Access to Document

10.4310/HHA.2018.v20.n2.a13

Cite this

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title = "On polyhedral product spaces over polyhedral joins",

abstract = " The construction of a simplicial complex given by polyhedral joins (introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen and Gitler{\textquoteright}s � -construction and simplicial wedge construction. This article gives a cohomological decomposition of a polyhedral product over a polyhedral join. A formula for the Hilbert–Poincar{\'e} series is given, which generalizes Ayzenberg{\textquoteright}s formula for the moment-angle complex. ",

keywords = "cohomology ring, moment-angle complex, simplicial complex, Stanley–Reisner ring, simplicial wedge construction",

author = "Elizabeth Vidaurre",

note = "This website requires Javascript in order to display and function properly. Please enable Javascript in your web browser. Pages: 259 - 280 DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n2.a13 Author Elizabeth Vidaurre (Department of Mathematics, University of Rochester, New York, U.S.A.) Abstract The construction of a simplicial complex given by polyhedral joins (introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen and Gitler's \$J\$-construction and simplicial wedge construction.",

year = "2018",

month = jun,

doi = "10.4310/HHA.2018.v20.n2.a13",

language = "American English",

volume = "20",

journal = "Homology, Homotopy and Applications",

issn = "1532-0081",

publisher = "International Press",

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PY - 2018/6

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N2 - The construction of a simplicial complex given by polyhedral joins (introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen and Gitler’s � -construction and simplicial wedge construction. This article gives a cohomological decomposition of a polyhedral product over a polyhedral join. A formula for the Hilbert–Poincaré series is given, which generalizes Ayzenberg’s formula for the moment-angle complex.

AB - The construction of a simplicial complex given by polyhedral joins (introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen and Gitler’s � -construction and simplicial wedge construction. This article gives a cohomological decomposition of a polyhedral product over a polyhedral join. A formula for the Hilbert–Poincaré series is given, which generalizes Ayzenberg’s formula for the moment-angle complex.

KW - cohomology ring

KW - moment-angle complex

KW - simplicial complex

KW - Stanley–Reisner ring

KW - simplicial wedge construction

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DO - 10.4310/HHA.2018.v20.n2.a13

M3 - Article

SN - 1532-0081

VL - 20

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

ER -