Selected publications in manifold theory
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This is a chronological list of significant publications in the theory of manifolds, It is the personal choice of Andrew Ranicki, and is thus very biased! The list is not intended to be encyclopedic: please contact Andrew if you have suggestions for additions/deletions. The dates listed are the publication dates, not necessarily when the work was actually created.
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
The first construction of a PL manifold without a 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 | Brieskorn | 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 |