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arXiv · 1109.2728

The homotopy type of the polyhedral product for shifted complexes

Jelena Grbic·Stephen Theriault
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Abstract

We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if K is a shifted simplicial complex on n vertices, X_1,..., X_n are spaces and CX_i is the cone on X_i, then the polyhedral product determined by K and the pairs (CX_i,X_i) is homotopy equivalent to a wedge of suspensions of smashes of the X_i's. This generalises earlier work of the two authors in the special case where each X_i is a loop space. Connections are made to toric topology, combinatorics, and classical homotopy theory.

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Jelena Grbic, Stephen Theriault. 2011-10-20. The homotopy type of the polyhedral product for shifted complexes. https://arxiv.org/abs/1109.2728

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