∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
symmetric monoidal (∞,1)-category of spectra
and
rational homotopy theory (equivariant, stable, parametrized, equivariant & stable, parametrized & stable)
Examples of Sullivan models in rational homotopy theory:
The generalization of the concept of nilpotent Lie algebra from Lie algebras to -algebras..
Under the formal duality between -algebras and their Chevalley-Eilenberg dgc-algebras, connective nilpotent -algebras correspond bijectively to the connected Sullivan models (Berglund 2015, Thm. 2.3).
The fundamental theorem of dgc-algebraic rational homotopy theory says that the homotopy theory of nilpotent -algebras of finite type over the rational numbers is equivalently that of rational nilpotent topological spaces of finite type.
Ezra Getzler, Def. 4.2 in: Lie theory for nilpotent algebras, Annals of Mathematics, 170 (2009), 271–301 (math.AT/0404003)
Alexander Berglund, Def. 2.1 in: Rational homotopy theory of mapping spaces via Lie theory for algebras, Homology, Homotopy and Applications, Volume 17 (2015) Number 2 (arXiv:1110.6145, doi:10.4310/HHA.2015.v17.n2.a16)
Last revised on July 22, 2021 at 17:46:15. See the history of this page for a list of all contributions to it.