On functional spaces whose source is in the classifying space of a commutative compact Lie group
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.
scientific article; zbMATH DE number 1560382
scientific article