Selected publications in manifold theory

Revision as of 16:37, 14 December 2010

This is a timeline of important publications in the theory of manifolds, including

• smooth manifolds,
• piecewise-linear manifolds;
• topological manifolds;
• homology manifolds.

See also:

• Chronology at MacTutor
• Geometry and topology at MacTutor
• timeline of events in manifold theory

1 Up to 1900

2 1900 - 1930

'

3 1930 - 1960

Year	Authors	Publication and remarks
1956	Milnor	On manifolds homeomorphic to the $<!-- COMMENT: To achieve a unified layout, along with using the template below, please observe the following: besides, $...$ and $$...$$, you should use two environments: - For statements like Theorem, Lemma, Definition etc., use e.g. {{beginthm|Theorem 1|(Milnor)}} ... ... ... {{endthm}}. - For references, use e.g. {{cite|Milnor1958b}}. END OF COMMENT --> {{Stub}} == Introduction == <wikitex>; ... </wikitex> == References == {{#RefList:}} [[Category:History]] </wikitex>7$-sphere Showed the existence of several smooth structures on a fixed topological manifold: in this case the $7$-sphere.

4 1961 - 1970

|- |1961 || Smale || Generalized Poincaré's conjecture in dimensions greater than four Proved that every smooth homotopy sphere of dimension 6 or more is homeomorphic to the standard sphere |- |1963 || Kervaire Milnor || Groups of homotopy spheres I Applied surgery theory to the diffeomorphism classification of smooth structures the n-sphere |}

5 1971 - 1980

6 1981 - 1990

7 1991 - 2000

8 2001 - present

9 Discussion

10 Footnotes

1. ↑ An interesting fact is that Milnor could easily have made this observation in his 1956 paper [Milnor1956] on $7$-spheres.

11 References