nLab
Sullivan conjecture

Contents

Context

Homotopy theory

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

Representation theory

Contents

Idea

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 using the Segal-Carlsson theorem was given in Carlsson 91

References

References

  • 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)

  • Gunnar Carlsson, Equivariant stable homotopy and Sullivan’s conjecture. Invent. Math. 103: 497–525, 1991 (dml:143867, pdf)

See also

Last revised on September 10, 2018 at 08:15:37. See the history of this page for a list of all contributions to it.