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

By A. Bahri, Martin Bendersky, Frederick R. Cohen, S. Gitler. 2010

72 citations recorded by the source corpus.

A combinatorial construction is used to analyze the properties of polyhedral products 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 which 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 literature.

Subfields: Computer Graphics and Computer-Aided Design, Discrete Mathematics and Combinatorics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/5e7b87ff105a9cdf027242b51bd10e859fd84ee7

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In Discrete Mathematics and Combinatorics

1. T. Panov
2. S. Theriault
3. J. Grbić
4. Suyoung Choi
5. Jie Wu
6. Hanchul Park
7. M. Masuda
8. V. Buchstaber

Citations in the corpus

• The homotopy types of moment-angle complexes for flag complexes (2012, background): “In [2], polyhedral products related to the simplicial wedge constriction were introduced and studied.”
• On the cohomology and their torsion of real toric objects (2013, background): “We briefly present the notion of K(J) of [1] here.”