xii INTRODUCTION is the characteristic Seifert pair. The bulk of Chapter IX is in giving a detailed proof of Theorem IX.17, which allows a characterization of the characteristic Seifert pair via homotopy classifications of maps. I con- clude Chapter IX with examples of the characteristic Seifert pair of some familiar 3-manifolds and some examples for caution. I think it is fair to say that I worked the hardest for the results of Chapter X. I guess what is good about this is that I am pleased with the outcome. For here, I present the generalized version of Waldhausen*s Theorem on deforming homotopy equivalences (X.7) hence, I have answered conjecture 13.10 of [He ] affirmatively and given a complete proof of this version of the theorem, which is due to T. Tucker (X.9). Moreover, I have been able to obtain a new proof of the beautiful theorem due originally to K. Johannson [Jo^] on the deformations of homotopy equivalences between Haken-manifolds with incompressible boundary (X.15 and X.21). This proof is inspired by observations of A. Swarup (VII.22 and VII.24). I also give many examples of "exotic" homotopy equivalences. Most of these examples are well-known. I have used standard terminology and notation except for the new terms that are introduced of course, here I give the required definitions and describe the new notation. The reader will find that I have included a lot of detail. However, if there were items that I felt might improve the presentation and I did not want to complete the detail, I set such items off as Exercises. This is in contrast to items labeled as Question in the case of a question, I simply do not know the answer.
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