A la Recherche de la Topologie Perdue: I. Du côté de chez Rohlin. II. Le côté de Casson

This book is a collection of papers previously difficult
to obtain and of fundamental importance in the theory
of 4-dimensional manifolds.
The first part contains a French translation of four 1952
papers by V. A. Rohlin announcing his famous result
on the signature of 4-dimensional manifolds. A detailed
commentary of these notes explains geometric methods
somewhat forgotten since then and gives new proofs
of classical 4-dimensional results. Also included are two
papers on more recent extensions of Rohlin's original
result.
The second part proposes an elementary exposition of the
most used corollary of the Atiyah-Singer theorem by
C. Gordon followed by an application of this result to
the study of knot cobordism by A. Casson and C. Gordon.
The book ends with a summary of the 1973—74
fundamental conferences of A. Casson which opened
up the way to the recent success of M. Freedman
and F. Quinn.
Table des matières
V. A. Rohlin (1919 - 1984) ix
Travaux de V. A. Rohlin xi
Introduction xv
I - Du côté de chez Rohlin
. Quatre articles de V. A. Rohlin (traduit du russe par
S. Ochanine) 3
. Commentaires sur les quatres articles précédents de
V. A. Rohlin, par L. Guillou et A. Marin 25
. Une extension d'un théorème de Rohlin sur la signature,
par L. Guillou et A. Marin 97
. An elementary proof of Rohlin's signature theorem and its
extension by Guillou and Marin, by Y. Matsumoto. ...... 119
2
CP /tf ou Kuiper et Massey au pays des coniques,
par A. Marin 141
Appendice
. Une histoire des rapports entre Rohlin et son théorème (telle
que racontée aux auteurs par 0. Viro et V. Harlamov) .... 153
II - Le côté de Casson
. On the G-signature theorem in dimension four, by C. Gordon . 159
Cobordism of classical knots, by A. Casson and C. Gordon . . 181
. Three lectures on new infinité constructions in 4-dimensional
manifolds, by A. Casson (notes prepared by L. Guillou). . . 201