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 Ranicki 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 on the n-sphere |
1965 | Novikov | Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds I
The topological invariance of the rational Pontrjagin classes. |
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 |