Xll
EDITOR'S FOREWORD TO THE SECOND EDITION
The book fulfilled five purposes, providing:
1. a coherent framework for relating the homotopy theory of manifolds to the
algebraic theory of quadratic forms, unifying many of the previous results;
2. a surgery obstruction theory for manifolds with arbitrary fundamental
group, including the exact sequence for the set of manifold structures
within a homotopy type, and many computations;
3. the extension of surgery theory from the differentiate and piecewise linear
categories to the topological category;
4. a survey of most of the activity in surgery up to 1970;
5. a setting for the subsequent development and applications of the surgery
classification of manifolds.
However, despite the book's great influence it is not regarded as an 'easy read'.
In this edition I have tried to lighten the heavy demands placed on the reader
by suggesting that §§0, 7,8, 9,12 could be omitted the first time round - it is
possible to take in a substantial proportion of the foundations of surgery theory
in Parts 1 and 2 and the applications in Part 3 without these chapters.
Readers unfamiliar with surgery theory should have the papers of Milnor [Ml2],
Kervaire and Milnor [K4] at hand, and see how the construction and classifica-
tion of exotic spheres fits into the general theory. Also, the books of Browder
[B24] and Novikov [N9] provide accounts of surgery from the vantage points of
two pioneers of the field.
My own experience with reading this book was somewhat unusual. I was a
first-year graduate student at Cambridge, working on Novikov's paper [N8],
when the book reached the bookshops in early 1971*. When I finally acquired
a copy, I was shocked to note that the very last reference in the book was to
[N8], so that in effect I read the book backwards. The book accompanied me
throughout my career as a graduate student (and beyond) - I always had it with
me on my visits home, and once my mother asked me: 'Haven't you finished
reading it yet?' My own research and books on surgery have been my response
to this book, which I have still not finished reading.
Preparing the second edition of the book was an even more daunting experience
than reading the first edition. It would be impossible to give a full account of
all the major developments in surgery which followed the first edition without
at least doubling the length of the book - the collections of papers [C7], [F10]
include surveys of many areas of surgery theory. In particular, I have not even
tried to do justice to the controlled and bounded theories (Quinn [Q6], Ferry and
Pedersen [F9]), which are among the most important developments in surgery
*I have a vivid memory of telephoning the Foyles bookshop in London in search of a copy,
and being directed to the medical department.
Previous Page Next Page