nLab differential graded objects - contents

differential graded objects

and

rational homotopy theory (equivariant, stable, parametrized, equivariant & stable, parametrized & stable)

dg-Algebra

• graded vector space

• differential graded vector space

• differential graded algebra

  • model structure on dgc-algebras

  • model structure on equivariant dgc-algebras

• differential graded coalgebra

  • model structure on dg-coalgebras

• differential graded Lie algebra

  • model structure on dg-Lie algebras

• L-∞ algebra

  • model structure for L-∞ algebras

• differential graded Hopf algebra

• bar and cobar construction

Rational spaces

• nilpotent space

• finite type

• rational space

  • formal space

• rationalization

PL de Rham complex

• differential forms on simplices

• PL de Rham complex

• Sullivan construction

  • Lie integration

• fundamental theorem of dg-algebraic rational homotopy theory

Sullivan models

• minimal$\,$Sullivan model

Examples of Sullivan models in rational homotopy theory:

• Sullivan model of an n-sphere

• Sullivan model of a spherical fibration

• Sullivan model of complex projective space

• Sullivan model of a classifying space

• Sullivan model of mapping space

• Sullivan model of free loop space

• Sullivan model of a suspension

• Sullivan model of a finite G-quotient

Related topics

• homotopy theory

• stable homotopy theory

• homological algebra

• ∞-Lie theory