Let X and Y be two topological spaces. We note that a discussion of the homotopy groups of the space of continuous functions from X to Y leads to a discussion of the algebra derivations from the cohomology algebra of Y to the cohomology algebra of X. This observation, and the Bousfield-Kan spectral sequence, allow us to apply the commutative algebra cohomology of André and Quillen to the study of the homotopy type of spaces of maps.
ASJC Scopus subject areas
- Algebra and Number Theory