On the homotopy of certain mapping spaces
type: Item
instance of: scholarly article
title: On the homotopy of certain mapping spaces
zbMATH Open document ID: 0667.55010
author: Seiya Sasao
published in: Kodai Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The author provides a method to compute the homotopy groups of certain subspaces of the space of based self-maps of the total space X in a principal G-bundle over the n-sphere. The method involves identifying the space obtained by collapsing a fibre in X to the base point with the one point union (wedge sum) of the n-sphere and the n-fold suspension of G, and the homotopy sequences for certain fibrations of mapping spaces. The main application is to the space of bundle maps of X into itself.
Mathematics Subject Classification ID: 55Q52
Mathematics Subject Classification ID: 55R10
Mathematics Subject Classification ID: 58D05
zbMATH DE Number: 4092342
zbMATH Keywords: homotopy groups of subspaces of the space of based self-maps of the total space in a principal bundle over the n-sphere
zbMATH Keywords: homotopy sequences for fibrations of mapping spaces
zbMATH Keywords: space of bundle maps
reviewed by: Vagn Lundsgaard Hansen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138038882
OpenAlex ID: W2002968967
cites work: A Study of Function Spaces by Spectral Sequences
cites work: Track Groups (I)
cites work: On Spaces of Maps between Complex Projective Spaces
cites work: The stable group of self-homotopy equivalences of sphere bundles over the sphere
cites work: The Homotopy of Map(Cp m , CP n )
cites work: Q5837351
cites work: On Spaces of Maps of n-Manifolds Into the n-Sphere
cites work: A generalization of the Hopf invariant
DOI: 10.2996/KMJ/1138038882
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description: scientific article; zbMATH DE number 4092342