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.

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 1980 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.