Exotic spheres

An exotic sphere is an n-dimensional differentiable manifold which is homeomorphic but not diffeomorphic to the standard n-sphere Sn.

  • On manifolds homeomorphic to the 7-sphere, by J.Milnor, Ann. of Math. (2) 64, 399--405 (1956)

  • Classification of (n-1)-connected 2n-dimensional manifolds and the discovery of the exotic spheres
    by J.Milnor, Surveys in Surgery Theory Theory, Vol. 1, Ann. of Math. Studies 145, 25--30 (2000)

  • Fifty years ago: topology in the 50's and 60's by J.Milnor (2006)

  • Differentiable manifolds which are homotopy spheres, by J.Milnor, Princeton notes (1959)

  • Differentiable structures on spheres, by J.Milnor, Am. J. Math. 81, 962--972 (1959)

  • Bernoulli numbers, homotopy groups, and a theorem of Rohlin by J.Milnor and M.Kervaire, Proc. 1958 Edinburgh ICM, 454--458 (1959)

  • The Kervaire-Milnor correspondence (1958--1961). Transcription.

  • A manifold which does not admit any differentiable structure, by M.Kervaire, Comm. Math. Helv. 34, 257--270 (1960)

  • A procedure for killing homotopy groups of differentiable manifolds, by J.Milnor, Proc. Sympos. Pure Math., Vol. III, 39--55, A.M.S. (1961)

  • Differentiable structures on the 15-sphere and Pontrjagin classes of certain manifolds, by N.Shimada, Nagoya Math. J. 12, 59--69 (1957)

  • 8-manifolds admitting no differentiable structure, by I.Tamura, J. Math. Soc. Japan 13, 377--382 (1961)

  • Remarks on differentiable structures on spheres, by I.Tamura, J. Math. Soc. Japan 13, 383--386 (1961)

  • Classification of (n-1)-connected 2n-manifolds by C.T.C. Wall, Ann. of Math. (2) 75, 163--189 (1962)

  • Groups of homotopy spheres I. by M.Kervaire and J.Milnor, Ann. of Math. (2) 77, 504--537 (1963)

  • Beispiele zur Differentialtopologie von Singularitäten by E. Brieskorn, Inv. Math. 2, 1--14 (1966)

  • O(n)-Mannigfaltigkeiten, exotische Sphären und Singularitäten by F.Hirzebruch and K.-H.Mayer, Springer Lecture Notes 57 (1968)

  • An invariant for almost-closed manifolds by D.Frank, Bull. Amer. Math. Soc. 74, 562--567 (1968)

  • On the homotopy groups of BPL and PL/O by G.Brumfiel, Ann. of Math. 88, 291--311 (1968)

  • Lectures on groups of homotopy spheres by J.Levine, Springer Lecture Notes 1126, 62--95 (1969/1985)

  • On the homotopy groups of BPL and PL/O III. by G.Brumfiel, Michigan Math. J. 17, 217--224 (1970)

  • Combinatorial Pontrjagin classes by J.Milnor and J.Stasheff, Chapter 20 of Characteristic Classes, Ann. of Math. Studies 76 (1974)

  • Cobordism theory and exotic spheres by J.Plotkin, Harvard Senior Thesis (1999)

  • Differentiable structures on manifolds by T.Lance, Surveys in Surgery Theory Theory, Vol. 1, Ann. of Math. Studies 145, 73--104 (2000)

  • The structure set by A.Ranicki, Chapter 13 of Algebraic and Geometric Surgery, Oxford (2002)

  • Exotic spheres and curvature by M.Joachim and D.J.Wraith, Bull. A.M.S. 45, 595--616 (2008)

  • On the work of Michel Kervaire in surgery and knot theory by A.Ranicki, Slides of lecture given at Kervaire memorial symposium, Geneva, 10-12 February, 2009.
    Addendum Exotic spheres and the Kervaire invariant (8 May 2009)