دانلود کتاب 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