Sullivan conjecture

In mathematics, "Sullivan conjecture" can refer to any of several results and conjectures prompted by homotopy theory work of Dennis Sullivan. A basic theme and motivation concerns the fixed point set in group actions of a finite group $G$. The most elementary formulation, however, is in terms of the classifying space $BG$ of such a group. Roughly speaking, it is difficult to map such a space $BG$ continuously into a finite CW complex $X$. Such a version of the Sullivan conjecture was first proved by Haynes Miller.

In 1984, Miller proved that the function space, carrying the compact-open topology, of base point-preserving mappings from $BG$ to $X$ is then weakly contractible.

External links

*Springer|title=Sullivan conjecture|id=s/s120300|first=Daniel H.|last= Gottlieb
* [http://books.google.com/books?id=rjMXVqEiA7MC&pg=PA67&lpg=PA67&dq=%22sullivan+conjecture%22&source=web&ots=nI3OJJQN2J&sig=DFx0MSsGdiyvyZlbHT825picIbU#PPA68,M1 Book extract]