On functional spaces whose source is in the classifying space of a commutative compact Lie group
type: Item
instance of: scholarly article
title: On functional spaces whose source is in the classifying space of a commutative compact Lie group
zbMATH Open document ID: 0967.55013
DOI: 10.1007/BF02698856
author: François-Xavier Dehon
author: Jean Lannes
published in: Publications Mathématiques
publication date: 2001-04-19T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104157
review text: The authors address an important question posed by W.G. Dwyer and C.W. Wilkerson on the cohomology of a mapping space with the classifying space of a finite abelian \(p\)-group as source space. They extend the question also to the case where the source space is the classifying space \(X\) of a torus. Here they prove among other things that the set of homotopy classes of maps from \(X\) to a simply connected space \(Y\) whose ordinary homology is zero in odd degrees and a finite-dimensional free abelian group in each even degree, and whose rational cohomology is polynomial, can be identified with the set of maps from the K-theory of \(Y\) to the K-theory of \(X\) which preserve the \(\lambda\)-ring structure. By necessity such results are of a rather technical nature.
Mathematics Subject Classification ID: 55R37
Mathematics Subject Classification ID: 55P99
zbMATH DE Number: 1560382
zbMATH Keywords: cohomology of a mapping space
reviewed by: Vagn Lundsgaard Hansen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1560382