André-Quillen cohomology and the homotopy groups of mapping spaces: understanding the E2-term of the Bousfield-Kan spectral sequence

Paul G. Goerss

doi:10.1016/0022-4049(90)90021-9

André-Quillen cohomology and the homotopy groups of mapping spaces: understanding the E₂-term of the Bousfield-Kan spectral sequence

Paul G. Goerss^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	113-153
Number of pages	41
Journal	Journal of Pure and Applied Algebra
Volume	63
Issue number	2
DOIs	https://doi.org/10.1016/0022-4049(90)90021-9
State	Published - Mar 12 1990

Funding

by the National Science Foundation. of Washington, Seattle, WA 98195, USA.

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/0022-4049(90)90021-9

Cite this

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abstract = "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 Andr{\'e} and Quillen to the study of the homotopy type of spaces of maps.",

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