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 . The most elementary formulation, however, is in terms of the classifying space of such a group. Roughly speaking, it is difficult to map such a space continuously into a finite CW complex . 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 to is then weakly contractible.
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