A theory of PWD-structures
type: Item
instance of: scholarly article
title: A theory of PWD-structures
zbMATH Open document ID: 1122.55004
author: Giora Dula
author: Howard J. Marcum
author: Peter Hilton
published in: Topology and its Applications
publication date: 2007-05-10T00:00:00Z
review text: A PWD (product-wedge diagonal) structure on a space \(X\) consists of a space \(D_nX\) and maps \(\rho: X \to D_nX\), \(\sigma: \vee_{i=1}^nX \to D_nX\), \(\tau: D_nX \to X^n\) such that \(\tau\sigma\) is homotopic to the inclusion \(\vee_{i=1}^nX \to X^n\) and \(\tau\rho: X \to X^n\) is homotopic to the diagonal. This structure generalizes some previosly known structures (Whitehead fat wedge, double mapping cylinder, etc.). The authors develop a general theory of PWD-structures. In particular, they obtain some results of Berstein--Hilton type.
reviewed by: Yuli Rudyak
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 55Q25
Mathematics Subject Classification ID: 55P65
zbMATH DE Number: 5151647
zbMATH Keywords: Berstein-- Hilton theorem
zbMATH Keywords: diagonal map
zbMATH Keywords: Hopf invariant
zbMATH Keywords: Lusternik--Schnirelmann category
zbMATH Keywords: fat wedge
MaRDI profile type: Publication
full work available at URL: j.topol.2006.11.008
OpenAlex ID: W2067101121
cites work: Category and generalized Hopf invariants
cites work: Q5522744
cites work: Q4421932
cites work: Q4409982
cites work: On Pierce-like idempotents and Hopf invariants
cites work: Q4409976
cites work: A\(_{\infty}\)-method in Lusternik-Schnirelmann category
cites work: Fibrations over double mapping cylinders
cites work: FUNCTORIAL PROPERTIES OF THE HOPF INVARIANT I
cites work: Joins, diagonals and Hopf invariants
cites work: Q4409988
cites work: Q5530417
DOI: 10.1016/J.TOPOL.2006.11.008
description: scientific article; zbMATH DE number 5151647