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.

UR - http://www.scopus.com/inward/record.url?scp=38249019612&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249019612&partnerID=8YFLogxK

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 -