and
rational homotopy theory (equivariant, stable, parametrized, equivariant & stable, parametrized & stable)
Examples of Sullivan models in rational homotopy theory:
The fundamental theorem of rational homotopy theory modeled by dgc-algebras.
(nilpotent and finite rational homotopy types)
Write
for the full subcategory of the classical homotopy category (homotopy category of the classical model structure on simplicial sets) on those homotopy types which are
nilpotent: is a nilpotent group
rational finite type: for all .
and
for the further full subcategory on those homotopy types that are already rational.
Similarly, write
for the full subcategory of the homotopy category of the projective model structure on connective dgc-algebras on those dgc-algebras which are
connected:
finite type: for all .
(fundamental theorem of dg-algebraic rational homotopy theory)
of the Quillen adjunction between simplicial sets and connective dgc-algebras (whose left adjoint is the PL de Rham complex-functor) has the following properties:
on connected, nilpotent rationally finite homotopy types (1) the derived adjunction unit is rationalization
on the full subcategories of nilpotent and finite rational homotopy types from Def. it restricts to an equivalence of categories:
(Bousfield-Gugenheim 76, Theorems 9.4 & 11.2)
Last revised on December 22, 2020 at 22:52:44. See the history of this page for a list of all contributions to it.