On PL DeRham Theory and Rational Homotopy Type

Download or read book On PL DeRham Theory and Rational Homotopy Type written by Aldridge Knight Bousfield and published by American Mathematical Soc.. This book was released on 1976 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rational [bold]PL de Rham theory of Sullivan is developed and generalized, using methods of Quillen's "homotopical algebra." For a field k of characteristic 0, a pair of contravariant adjoint functors A : (Simplicial sets) [right arrow over left arrow] (Commutative DG k-algebras) : F is obtained which pass to the appropriate homotopy categories. When k is the field of rationals, these functors induce equivalence between the appropriate simplicial and algebraic rational homotopy categories. The theory is not restricted to simply connected spaces. It is closely related to the theory of "rational localization" (for nilpotent spaces) and "rational completion" in general.