Selected publications in manifold theory
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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 1890
Year | Authors | Publication and remarks |
---|---|---|
1868 | Riemann | Über die Hypothesen, welche der Geometrie zugrunde liegen |
2 1891 - 1930
Year | Authors | Publication and remarks |
---|---|---|
1899 | Poincaré | Complément à l'Analysis situs. |
1907 | Dehn Heegaard | Analysis situs |
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 || Atiyah || Bordism and cobordism |- |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 |- |1966 || [ Brieskonr] || Beispiele zur Differentialtopologie von Singularitäten |- |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 |
1996 | [ Casson] | Generalisations and applications of block bundles |
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.