Polyhedral products and features of their homotopy theory

Authored by: Anthony Bahri , Martin Bendersky , Frederick R. Cohen

Handbook of Homotopy Theory

Print publication date:  December  2019
Online publication date:  December  2019

Print ISBN: 9780815369707
eBook ISBN: 9781351251624
Adobe ISBN:




A polyhedral product is a natural topological subspace of a Cartesian product, determined by a simplicial complex K and a family of pointed pairs of spaces (X i , A i ), one for each vertex of K. As noted in [126], in the special case that A i is a basepoint for X i , the polyhedral product mediates between the product X 1 × X 2 × · · · × X m when K is the full (m − 1)-simplex, and the wedge X 1X 2∨ · · · ∨X m when K consists of m discrete points.

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