Editor's foreword to the second edition

The publication of this book in 1970 marked the culmination of a particularly

exciting period in the history of the topology of manifolds. The world of high-

dimensional manifolds had been opened up to the classification methods of

algebraic topology by

• Thorn's work on transversality and cobordism (1952)

• the signature theorem of Hirzebruch (1954)

• the discovery of exotic spheres by Milnor (1956).

In the 1960's there had been an explosive growth of interest in the surgery

method of understanding the homotopy types of manifolds (initially in the dif-

ferentiable category), including such results as

• the /i-cobordism theorem of Smale (1960)

• the classification of exotic spheres by Kervaire and Milnor (1962)

• Browder's converse to the Hirzebruch signature theorem for the existence

of a manifold in a simply connected homotopy type (1962)

• Novikov's classification of manifold structures within a simply connected

homotopy type (1962)

• the s-cobordism theorem of Barden, Mazur and Stallings (1964)

• Novikov's proof of the topological invariance of the rational Pontrjagin

classes of differentiable manifolds (1965)

• the fibering theorems of Browder and Levine (1966) and Farrell (1967)

• Sullivan's exact sequence for the set of manifold structures within a simply

connected homotopy type (1966)

• Casson and Sullivan's disproof of the Hauptvermutung for piecewise linear

manifolds (1967)

• Wall's classification of homotopy tori (1969)

• Kirby and Siebenmann's classification theory of topological manifolds (1970).

XI