higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
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?
For $G$ a suitable equivariance group, the infinite projective G-space is the projective G-space corresponding to the “complete infinite $G$-representation”, namely to a given G-universe.
Over the ground field of complex numbers this is the generalization to topological G-spaces/$G$-equivariant homotopy theory of the infinite complex projective space, hence the classifying space for complex line bundles, now classifying equivariant complex line bundles.
(infinite complex projective G-space)
For $G$ an abelian compact Lie group, let
be the G-universe being the infinite direct sum of all complex 1-dimensional linear representations of $G$, regarded as a topological G-space with toplogy the colimit of its finite-dimensional linear subspaces.
Then the infinite complex projective G-space is the colimit
of the projective G-spaces for all the finite-dimensional $G$-linear representations inside the G-universe (1).
(e.g. Greenlees 01, Sec. 9.2)
Created on November 12, 2020 at 13:35:09. See the history of this page for a list of all contributions to it.