The homotopy type of the polyhedral product for shifted complexes

Details The homotopy type of the polyhedral product for shifted complexes The homotopy type of the polyhedral product for shifted complexes

2011-09-13

arxiv.org/abs/1109.2728v2

Mathematics

Algebraic Topology

27 pages, typos corrected, Section 8 improved

Scientific paper

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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