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

• Gottlieb, Daniel H. (2001), "Sullivan conjecture", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104, http://www.encyclopediaofmath.org/index.php?title=s/s120300 
• Book extract