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?
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
and
rational homotopy theory (equivariant, stable, parametrized, equivariant & stable, parametrized & stable)
Examples of Sullivan models in rational homotopy theory:
Let be a finite group.
There is a model category-structure on the category
of connective -equivariant cochain complexes (i.e. with differential of degree +1) over the rational numbers, whose
– weak equivalences are the quasi-isomorphisms over each ;
– cofibrations are the positive-degree wise injections over each ;
– fibrations are the morphisms which over each are degree-wise surjections whose degreewise kernels are injective objects (in the category of vector G-spaces).
For the trivial group, this reduces to the injective model structure on connective cochain complexes.
Last revised on September 25, 2020 at 12:42:05. See the history of this page for a list of all contributions to it.