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?
homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
and
rational homotopy theory (equivariant, stable, parametrized, equivariant & stable, parametrized & stable)
Examples of Sullivan models in rational homotopy theory:
Let be a finite group.
An -equivariant chain complex is a functor
from the orbit category of to a category of chain complexes.
Georgia Triantafillou, Equivariant minimal models, Trans. Amer. Math. Soc. vol 274 pp 509-532 (1982) (jstor:1999119)
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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