Exotic spheres
An exotic sphere is an n-dimensional differentiable manifold which is
homeomorphic but not diffeomorphic to the standard n-sphere
Sn.
The articles on exotic spheres on the
Wikipedia and the
Manifold Atlas Project.
Bulletin of the AMS Volume 52 Number 4
On manifolds homeomorphic to the 7-sphere,
by J.Milnor, Ann. of Math. (2) 64, 399--405 (1956)
Hedrick Lectures on Differential Topology by J. Milnor (1965)
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)
Spheres Abel Prize Lecture by J. Milnor (2011)
Differential topology 46 years later by J.Milnor, Notices A.M.S. 58, 804--809 (2011)
The tabulation of exotic spheres in the On-Line Encyclopedia of Integer Sequences.
The number
of differential structures on the -sphere, from
the Online Encyclopedia of Integer Sequences
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)
An invariant for certain smooth manifolds
by J. Eells and N. Kuiper, Ann. Mat. Pura Appl. (4) 60, 93-110 (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)
Singularities and exotic spheres
by F. Hirzebruch, Seminaire Bourbaki, Vol. 10, Exp. 314, 13-32 (1967)
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)
An exotic sphere with nonnegative sectional
curvature.
by D.Gromoll and W.Meyer, Ann. of Maths. 100, 401--406 (1974)
Combinatorial Pontrjagin classes by
J.Milnor and J.Stasheff, Chapter 20 of Characteristic Classes,
Ann. of Math. Studies 76 (1974)
Spheres exotiques et l'espace de Whitehead
(English translation) by M.Weiss, C.R. Acad. Sci. Paris Ser. I. Math. 303,
885--888 (1986)
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)
A minimal Brieskorn 5-sphere in the
Gromoll-Meyer sphere and its applications.
by C.Duran and T.Püttmann, Michigan Math. J. 56, 419--451 (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)
An introduction to exotic spheres and singularities
by A.Ranicki, Slides of lecture given in Edinburgh, 4 May 2012
Dusa McDuff and Jack Milnor (Somewhere in Scotland, 2011)