Homology, Homotopy and Applications

Volume 17 (2015)

Number 2

Operations on polyhedral products and a new topological construction of infinite families of toric manifolds

Pages: 137 – 160

DOI: https://dx.doi.org/10.4310/HHA.2015.v17.n2.a8

Authors

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

M. Bendersky (Department of Mathematics, Hunter College, City University of New York, N.Y., U.S.A.)

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

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

Abstract

A combinatorial construction is used to analyze the properties of polyhedral products [1] and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of infinite families of toric manifolds, associated to a given one, in a way that simplifies the combinatorial input and, consequently, the presentation of the cohomology rings. The new input is the interaction of a purely combinatorial construction with natural associated geometric constructions related to polyhedral products and toric manifolds. Applications of the methods and results developed here have appeared in [24, 25, 15, 18, 10, 23], and [19].

Keywords

polyhedral product, moment-angle complex, moment-angle manifold, quasitoric manifold, toric manifold, quasitoric manifold, smooth toric variety, non-singular toric variety, fan, simplicial wedge, join

2010 Mathematics Subject Classification

Primary 13F55, 14M25, 52B11, 55N10, 55U10. Secondary 14F45, 55T10.

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Published 3 December 2015