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 Sullivan conjecture (due to Dennis Sullivan, now a theorem due to Miller 84) states that – under certain conditions and after suitable p-adic completion – the canonical map for a G-space from its ordinary fixed points to its homotopy fixed points is a weak homotopy equivalence.
A proof was given in Carlsson 91, using the Segal-Carlsson theorem.
Haynes Miller, The Sullivan conjecture on maps from classifying spaces, Annals of Mathematics Second Series, Vol. 120, No. 1 (Jul., 1984), pp. 39-87 (jstor:2007071)
Gunnar Carlsson, Equivariant stable homotopy and Sullivan’s conjecture. Invent. Math. 103: 497–525, 1991 (dml:143867, pdf)
See also
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