Nice and lazy cell attachments
type: Item
instance of: scholarly article
title: Nice and lazy cell attachments
zbMATH Open document ID: 0859.55008
DOI: 10.1016/0022-4049(95)00131-X
author: Jean-Michel Lemaire
author: Kathryn Hess
published in: Journal of Pure and Applied Algebra
publication date: 1996-11-13T00:00:00Z
review text: Let \(X\) be a 1-connected CW-complex of finite type and let \(f: S^n\to X\) be a continuous map, \(n\geq 2\). In this paper the authors consider the map \(H_*\Omega i:H_* (\Omega X; \mathbb{R}) \to H_*(\Omega Y; \mathbb{R})\), where \(i\) denotes the injection of \(X\) into \(Y=X \cup_f e^{n+1}\). The cell attachment \(f\) is called lazy if the connecting map \(\delta: \Omega Y \to F\) of the Puppe sequence \(\Omega Y \to F\to Y @>i>> Y\) induces the trivial map in homology, and is called nice if \(H_*i: H_*(\Omega X; \mathbb{R})/(f') \to H_* (\Omega Y; \mathbb{R})\) is an injection; here \(f'\) is the element of \(H_{n-1} (\Omega X; \mathbb{R})\) induced by \(f\). The authors define laziness algebraically and topologically. They give algebraic criteria for laziness and interesting examples of cell attachments.
Mathematics Subject Classification ID: 55P35
zbMATH DE Number: 932635
zbMATH Keywords: cell attachment
zbMATH Keywords: loop space homology
reviewed by: Yves Félix
MaRDI profile type: Publication
cites work: On the chain algebra of a loop space
cites work: Non-commutative graded algebras and their Hilbert series
cites work: Q3715232
cites work: Presentations of algebras and the Whitehead \(\varGamma\)-functor for chain algebras
cites work: ON THE PONTRYAGIN ALGEBRA OF THE LOOPS ON A SPACE WITH A CELL ATTACHED
cites work: Q4022774
cites work: Sur l'homologie de l'espace des lacets d'une variété compacte
cites work: Module d'holonomie d'une fibration
cites work: Suites inertes dans les algèbres de Lie grasuées. ("Autopsie d'un meurtre II").
cites work: Q3803828
cites work: The fibre of a cell attachment
cites work: Obstructions to homotopy equivalences
cites work: Algèbres connexes et homologie des espaces de lacets
cites work: «Autopsie d'un meurtre» dans l'homologie d'une algèbre de chaînes
cites work: On adding relations to homotopy groups
description: scientific article; zbMATH DE number 932635