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Topological library. Part 2: Characteristic classes and smooth structures on manifolds. Translated by V. O. Manturov. (English) Zbl 1195.57004
This is the second of a planned three volume series reprinting selected foundational papers in topology from the period 1950 to 1970. The first volume [Topological library. Part 1: Cobordisms and their applications. Series on Knots and Everything 39. Hackensack, NJ: World Scientific. (2007; Zbl 1121.55003)] concentrated on the role of cobordism in stable homotopy theory. The present volume reprints six papers playing a critical role in the study of smooth structures on manifolds and the use of characteristic classes in that study together with a brief introduction by S. P. Novikov. The papers are [J. Milnor, “On manifolds homeomorphic to the 7-sphere”, Ann. Math. 64, 399–405 (1956; Zbl 0072.18402), M. Kervaire and J. Milnor, “Groups of homotopy spheres I.” Ann. Math. 77, 504–537 (1963; Zbl 0115.40505), S. P. Novikov, “Homotopically equivalent smooth manifolds,” Izv. Akad. Nauk SSSR, Ser. Mat. 28, 365–474 (1964; Zbl 0151.32103), “Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds,” ibid. 29, 1373–1388 (1965; Zbl 0146.19601), ”On manifolds with free abelian fundamental group and their applications.” Am. Math. Soc., Transl., II. Ser. 71, 1-42 (1968); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 30, 207-246 (1966; Zbl 0199.58202), R. Kirby, ”Stable homeomorphisms and the annulus conjecture,” Ann. Math. 89, 575–582 (1969; Zbl 0176.22004)].

57-03 History of manifolds and cell complexes
01A75 Collected or selected works; reprintings or translations of classics
57N65 Algebraic topology of manifolds
00B15 Collections of articles of miscellaneous specific interest