THE NIELSEN THEOREM FOR SEIFERT FIBERED SPACES OVER LOCALLY SYMMETRIC SPACES

THE NIELSEN THEOREM FOR SEIFERT FIBERED SPACES OVER LOCALLY SYMMETRIC SPACES

In this note the geometric realization of a finite group of homotopy classes of self homotopy equivalences by a finite group of diffeomorphisms is investigated. In order for this to be accomplished an algebraic condition, which guarantees a certain group extension exists, must be satisfied. It is shown for a geometrically interesting class of aspherical manifolds, called injective Seifert fiber spaces over a locally symmetric space, that this necessary algebraic condition is also sufficient for geometric realization.

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