Polyhedral products and features of their homotopy theory
Abstract
A polyhedral product is a natural subspace of a Cartesian product that is specified by a simplicial complex. The modern formalism arose as a generalization of the spaces known as moment-angle complexes which were developed within the nascent subject of toric topology. This field, which began as a topological approach to toric geometry and aspects of symplectic geometry, has expanded rapidly in recent years. The investigation of polyhedral products and their homotopy theoretic properties has developed to the point where they are studied in various fields of mathematics far removed from their origin. In this survey, we provide a brief historical overview of the development of this subject, summarize many of the main results and describe applications.
Keywords
Cite
@article{arxiv.1903.04114,
title = {Polyhedral products and features of their homotopy theory},
author = {A. Bahri and M. Bendersky and F. R. Cohen},
journal= {arXiv preprint arXiv:1903.04114},
year = {2024}
}
Comments
A serious typo in Theorem 9.3 is corrected. This article has appeared in the Handbook of Homotopy Theory