geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
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:
Let be a finite group.
A -equivariant dgc-algebra in the sense of equivariant rational homotopy theory is a functor
from the orbit category of to the category of dgc-algebras.
(equivariant PL de Rham complex)
Let be a simplicial set equipped with -action, for instance the singular simplicial set of a topological G-space.
The equivariant PL de Rham complex of is the equivariant dgc-algebra given as the functor from the orbit category of to the category of dgc-algebras
which to a coset space assigns the PL de Rham complex of the -fixed locus .
Georgia Triantafillou, Equivariant minimal models, Trans. Amer. Math. Soc. vol 274 pp 509-532 (1982) (jstor:1999119)
Marek Golasiński, Componentwise injective models of functors to DGAs, Colloquium Mathematicum, Vol. 73, No. 1 (1997) (dml:21048, pdf)
Marek Golasiński, Injective models of -disconnected simplicial sets, Annales de l’Institut Fourier, Volume 47 (1997) no. 5, p. 1491-1522 (numdam:AIF_1997__47_5_1491_0)
Laura Scull, A model category structure for equivariant algebraic models, Transactions of the American Mathematical Society 360 (5), 2505-2525, 2008 (doi:10.1090/S0002-9947-07-04421-2)
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