Selected publications in manifold theory
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|1965 || [http://www-history.mcs.st-and.ac.uk/Biographies/Novikov_Sergi.html Novikov] || {{citeD2|Novikov1965|Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds I}} | |1965 || [http://www-history.mcs.st-and.ac.uk/Biographies/Novikov_Sergi.html Novikov] || {{citeD2|Novikov1965|Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds I}} | ||
+ | |- | ||
+ | |1968 || [http://www-history.mcs.st-and.ac.uk/Biographies/Atiyah.html Atiyah] [http://www-history.mcs.st-and.ac.uk/Biographies/Singer.html Singer] || {{citeD2|Atiyah&Singer1968|The index of elliptic operators I}} | ||
|} | |} | ||
</wikitex> | </wikitex> |
Revision as of 17:46, 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
Contents |
1 Up to 1900
Year | Authors | Publication and remarks |
---|---|---|
1868 | Riemann | Über die Hypothesen, welche der Geometrie zugrunde liegen |
2 1900 - 1930
Year | Authors | Publication and remarks |
---|---|---|
1904 | Poincaré | Cinquieme |
1908 | Tietze | Über die topologischen Invarianten mehrdimensionaler Mannigfaltigkeiten |
3 1930 - 1960
Year | Authors | Publication and remarks |
---|---|---|
1926 | Lefschetz | Intersections and transformations of complexes and manifolds |
1931 | Hopf | Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche |
1931 | Morse | The critical points of a function of variables |
1944 | Whitney | The self-intersections of a smooth -manifold in -space |
1947 | Chern | On the characteristic classes of Riemannian manifolds |
1953 | Hirzebruch | On Steenrod's reduced powers, the index of inertia and the Todd genus |
1954 | Thom | Quelques propriétés globales des variétés différentiables |
1956 | Milnor | On manifolds homeomorphic to the -sphere
Showed the existence of several smooth structures on a fixed topological manifold: in this case the -sphere. |
1959 | Pontryagin | Smooth manifolds and their applications in homotopy theory |
4 1961 - 1970
Year | Authors | Publication and remarks |
---|---|---|
1960 | Kervaire | A manifold which does not admit any differentiable structure
Used surgery to find a PL manifold in dimension 10 which admits no smooth structure |
|- |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 |- |1965 || Novikov || Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds I |- |1968 || Atiyah Singer || The index of elliptic operators I |}
5 1971 - 1980
Year | Authors | Publication and remarks |
---|---|---|
19?? | ... | ... |
6 1981 - 1990
Year | Authors | Publication and remarks |
---|---|---|
1982 | Freedman | The topology of four-dimensional manifolds
Proves the Poincaré conjecture in dimension 4 |
1983 | Donaldson | An application of gauge theory to four-dimensional topology |
7 1991 - 2000
Year | Authors | Publication and remarks |
---|---|---|
19?? | ... | ... |
8 2001 - present
Year | Authors | Publication and remarks |
---|---|---|
20?? | ... | ... |
9 Discussion
10 Footnotes
- ↑ An interesting fact is that Milnor could easily have made this observation in his 1956 paper [Milnor1956] on $7$-spheres.