TY - JOUR
T1 - André-Quillen cohomology and the homotopy groups of mapping spaces
T2 - understanding the E2-term of the Bousfield-Kan spectral sequence
AU - Goerss, Paul G.
N1 - Funding Information:
by the National Science Foundation. of Washington, Seattle, WA 98195, USA.
PY - 1990/3/12
Y1 - 1990/3/12
N2 - 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.
AB - 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.
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U2 - 10.1016/0022-4049(90)90021-9
DO - 10.1016/0022-4049(90)90021-9
M3 - Article
AN - SCOPUS:38249019612
VL - 63
SP - 113
EP - 153
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 2
ER -