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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, Encyclopaedia of Mathematics, Springer, ISBN 978-1556080104, http://eom.springer.de/s/s120300.htm  Book extract This topology-related article is a stub. You can help Wikipedia by expanding it.v · d · e