Solving four-dimensional surgery problems using controlled theory

In this paper, the controlled surgery sequence of Ranicki, Pedersen, and Quinn is applied to the solution of surgery problems in dimension four when the fundamental group is not known to be good. Our examples concern free non-Abelian fundamental groups, surface fundamental groups, and special knot groups. Using results from our earlier paper (joint with Spaggiari), we state a general result from which our examples follow. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 221–236, 2005.