Selected publications in manifold theory
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|1908 || [http://www-history.mcs.st-and.ac.uk/Biographies/Tietze.html Tietze] || {{citeD2|Tietze1908|Über die topologischen Invarianten mehrdimensionaler Mannigfaltigkeiten}} | |1908 || [http://www-history.mcs.st-and.ac.uk/Biographies/Tietze.html Tietze] || {{citeD2|Tietze1908|Über die topologischen Invarianten mehrdimensionaler Mannigfaltigkeiten}} | ||
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| + | |1915 || [http://www-history.mcs.st-and.ac.uk/Biographies/Alexander.html Alexander] || {{citeD2|Alexander1915|A proof of the invariance of certain constants of analysis situs}} | ||
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Revision as of 11:17, 16 December 2010
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The user responsible for this page is Ranicki. No other user may edit this page at present. |
This is a chronological list of important publications in the theory of manifold. The list is not intended to be encyclopedic: please contact the author if you have suggestions.
The term manifold includes
- 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 |
| 1915 | Alexander | A proof of the invariance of certain constants of analysis situs |
3 1930 - 1960
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 |- |1962 || [Browder] || Homotopy type of differentiable manifolds |- |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 |- |1970 || [ Sullivan] || Geometric topology: localization, periodicity and Galois symmetry |- |1970 || Wall || Surgery on compact manifolds |}
5 1971 - 1980
| Year | Authors | Publication and remarks |
|---|---|---|
| 1974 | Chapman | Topological invariance of Whitehead torsion |
| 1977 | [ Kirby] [ Siebenmann] | Foundational essays on topological manifolds, smoothings, and triangulations |
| 1978 | [ Waldhausen] | Algebraic  -theory of topological spaces I
|
| 1980 | [ Edwards] | The topology of manifolds and cell-like maps |
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 |
| 1988 | [ Quinn] | Topological transversality holds in all dimensions |
7 1991 - 2000
| Year | Authors | Publication and remarks |
|---|---|---|
| 1993 | [ Farrell] [ Jones] | Topological rigidity for compact non-positively curved manifolds |
8 2001 - present
| Year | Authors | Publication and remarks |
|---|---|---|
| 2002 | Perelman | The entropy formula for the Ricci flow and its geometric applications |
| 2009 | [ Hill] [Hopkins] [Ravenel] | On the non-existence of elements of Kervaire invariant one |
9 Discussion
10 Footnotes
- ↑ An interesting fact is that Milnor might well used the manifolds in his 1956 paper [Milnor1956] on $7$-spheres to give examples of non-smoothable PL-manifolds.
