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
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 CW-approximation from plain homotopy theory to -equivariant homotopy theory is called -CW approximation:
For suitable equivariance groups , every topological G-space receives a -equivariant function from a G-CW complex , such that this restricts to a weak homotopy equivalence on -fixed loci, for all suitable subgroups .
This should hold for a compact Lie group (such as a finite group) and ranging over its closed subgroups.
Last revised on August 14, 2021 at 13:26:39. See the history of this page for a list of all contributions to it.