# nLab Sullivan conjecture

Contents

### Context

#### Representation theory

representation theory

geometric 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 was given in Carlsson 91, using the Segal-Carlsson theorem.

## 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:2007071)

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