On the splitting of mapping spaces between classifying spaces. I
type: Item
instance of: scholarly article
title: On the splitting of mapping spaces between classifying spaces. I
zbMATH Open document ID: 0633.55012
author: Norio Iwase
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1987-01-01T00:00:00Z
review text: If H is a simple Lie group of rank 1 and \(G_ 1\), \(G_ 2\) are compact, connected Lie groups with finite fundamental groups, it is proved that in both the free and based categories, the space of mappings from \(B(G_ 1\times G_ 2)\) to BH is weakly equivalent to the push out over BH (free) or wedge (based) of the mapping spaces of \(BG_ 1\) and \(BG_ 2\) into BH. One of the corollaries is that the set of homotopy classes of maps from the product of h copies of \(HP^{\infty}\) to k copies of \(HP^{\infty}\) is equivalent to the set of (k\(\times h)\)-matrices with entries equal to 0 or \((2r+1)^ 2\) for any \(r\in Z\). The proofs use many recent results in the literature, particularly work on the ``Sullivan conjecture'' associated with the names of Miller and Zabrodsky and also cohomology models of classifying spaces of connected Lie groups using locally finite groups due to Friedlander and Mislin.
reviewed by: J. R. Hubbuck
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 55S37
Mathematics Subject Classification ID: 55Q05
zbMATH DE Number: 4030505
zbMATH Keywords: simple Lie group of rank 1
zbMATH Keywords: compact, connected Lie groups with finite fundamental groups
zbMATH Keywords: mapping spaces
zbMATH Keywords: Sullivan conjecture
zbMATH Keywords: classifying spaces of connected Lie groups
zbMATH Keywords: locally finite groups
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195176439
OpenAlex ID: W2014171464
cites work: Q5842420
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DOI: 10.2977/PRIMS/1195176439
description: scientific article; zbMATH DE number 4030505