Sullivan conjecture

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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.

[edit] External links

• Gottlieb, Daniel H. (2001), “Sullivan conjecture”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104 
• Book extract