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?
The generalization of the stable homotopy category from stable homotopy theory to equivariant stable homotopy theory.
A homomorphism between two G-spectra, indexed on a G-universe , is called an equivariant weak homotopy equivalence if the following equivalent conditions hold
For each the component map induces ordinary weak homotopy equivalences on all fixed point spaces for all closed subgroups .
For each and each closed subgroup the morphism induces an isomorphism of Mackey functors of equivariant homotopy groups .
(The equivalence of these conditions is part of the equivariant Whitehead theorem.)
The -equivariant stable homotopy category is the homotopy category of G-spectra with respect to these weak equivalences.
The full subcategory of the equivariant stable homotopy category on the objects of the form
is, as an additive category, the domain of Mackey functors, such as the equivariant homotopy group-functors.
John Greenlees, Peter May, section 2 of Equivariant stable homotopy theory, in I.M. James (ed.), Handbook of Algebraic Topology , pp. 279-325. 1995. (pdf)
Anna Marie Bohmann, Basic notions of equivariant stable homotopy theory, (pdf)
Last revised on December 14, 2020 at 20:05:11. See the history of this page for a list of all contributions to it.