SMF

André-Quillen cohomology and the Bousfield-Kan spectral sequence

André-Quillen cohomology and the Bousfield-Kan spectral sequence

Paul G. GOERSS
  • Année : 1990
  • Tome : 191
  • Format : Papier, Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 18G50, 55T15, 55Q15
  • Pages : 109-209
  • DOI : 10.24033/ast.53

This paper undertakes to exploit the observation that the non-abelian homological algebra of Quillen and, in particular, the commutative algebra homology of André and Quillen provides a framework for discussing the unstable Adams spectral sequence of Bousfield and Kan. We take this observation in a variety of directions ; for instance, we show that the long exact “transitivity sequence” in the sequence of a fibration, and we show that a product in André-Quillen cohomology is related to the homotopy long exact sequence of a fibration, and we show that a product in André-Quillen cohomology can be used to compute the Whitehead product in homotopy.

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