Selected publications in manifold theory
From Manifold Atlas
(Difference between revisions)
m (→1961 - 1970) |
m |
||
| (38 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Authors|Ranicki}} | {{Authors|Ranicki}} | ||
| − | This is a chronological list of | + | This is a chronological list of significant publications in the theory of [[Wikipedia:manifold|manifolds]]: it is the personal choice of Andrew Ranicki, and is thus very biased! |
| + | |||
| + | The list is not intended to be encyclopedic: please contact [mailto:a.ranicki@ed.ac.uk 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 | The term ''manifold'' includes | ||
| − | * [[Wikipedia: | + | * [[Wikipedia:smooth_manifold|smooth]] manifolds, |
| − | * [[Wikipedia:piecewise- | + | * [[Wikipedia:piecewise-linear_manifold|piecewise-linear]] manifolds, |
| − | * [[topological | + | * [[Wikipedia:topological_manifold|topological]] manifolds, |
| − | * [[homology | + | * [[Wikipedia:homology_manifold|homology]] manifolds. |
See also: | See also: | ||
* [http://www-history.mcs.st-and.ac.uk/Chronology/index.html Chronology] at MacTutor | * [http://www-history.mcs.st-and.ac.uk/Chronology/index.html Chronology] at MacTutor | ||
| Line 29: | Line 33: | ||
! Publication and remarks | ! Publication and remarks | ||
|- | |- | ||
| − | | 1899 || [http://www-history.mcs.st-and.ac.uk/Biographies/Poincare.html Poincaré] || {{citeD2| | + | | 1899 || [http://www-history.mcs.st-and.ac.uk/Biographies/Poincare.html Poincaré] || {{citeD2|Poincaré1899|Complément à l'Analysis situs.}} |
| + | |- | ||
| + | |1907 || [http://www-history.mcs.st-and.ac.uk/Biographies/Dehn.html Dehn] [http://www-history.mcs.st-and.ac.uk/Biographies/Heegaard.html Heegaard] || {{citeD2|Dehn&Heegaard1907|Analysis situs}} | ||
|- | |- | ||
|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}} | ||
| Line 60: | Line 66: | ||
|1947 || [http://www-history.mcs.st-and.ac.uk/Biographies/Chern.html Chern] || {{citeD2|Chern1947|On the characteristic classes of Riemannian manifolds}} | |1947 || [http://www-history.mcs.st-and.ac.uk/Biographies/Chern.html Chern] || {{citeD2|Chern1947|On the characteristic classes of Riemannian manifolds}} | ||
|- | |- | ||
| − | |1952 || [http://en.wikipedia.org/wiki/Rochlin Rokhlin] || {{citeD2| | + | |1950 || [http://en.wikipedia.org/wiki/Whitehead_Henry Whitehead]|| {{citeD2|Whitehead1950|Simple homotopy types}} |
| + | |- | ||
| + | |1952 || [http://en.wikipedia.org/wiki/Rochlin Rokhlin] || {{citeD2|Rohlin1952|New results in the theory of four-dimensional manifolds}} | ||
|- | |- | ||
|1953 || [http://www-history.mcs.st-and.ac.uk/Biographies/Hirzebruch.html Hirzebruch] || {{citeD2|Hirzebruch1953a|On Steenrod's reduced powers, the index of inertia and the Todd genus}} | |1953 || [http://www-history.mcs.st-and.ac.uk/Biographies/Hirzebruch.html Hirzebruch] || {{citeD2|Hirzebruch1953a|On Steenrod's reduced powers, the index of inertia and the Todd genus}} | ||
| Line 85: | Line 93: | ||
|- | |- | ||
|1960 || [http://en.wikipedia.org/wiki/Kervaire Kervaire] || {{citeD2|Kervaire1960a|A manifold which does not admit any differentiable structure}} | |1960 || [http://en.wikipedia.org/wiki/Kervaire Kervaire] || {{citeD2|Kervaire1960a|A manifold which does not admit any differentiable structure}} | ||
| − | + | The first construction of a PL manifold without a smooth structure. | |
| + | |- | ||
| + | |1961 || [http://www-history.mcs.st-and.ac.uk/Biographies/Atiyah.html Atiyah] || {{citeD2|Atiyah1961|Bordism and cobordism}} | ||
|- | |- | ||
|1961 || [http://www-history.mcs.st-and.ac.uk/Biographies/Smale.html Smale] || {{citeD2|Smale1961|Generalized Poincaré's conjecture in dimensions greater than four}} | |1961 || [http://www-history.mcs.st-and.ac.uk/Biographies/Smale.html Smale] || {{citeD2|Smale1961|Generalized Poincaré's conjecture in dimensions greater than four}} | ||
| Line 93: | Line 103: | ||
|- | |- | ||
|1963 || [http://en.wikipedia.org/wiki/Kervaire Kervaire] [http://www-history.mcs.st-and.ac.uk/Biographies/Milnor.html Milnor] || {{citeD2|Kervaire&Milnor1963|Groups of homotopy spheres I}} | |1963 || [http://en.wikipedia.org/wiki/Kervaire Kervaire] [http://www-history.mcs.st-and.ac.uk/Biographies/Milnor.html Milnor] || {{citeD2|Kervaire&Milnor1963|Groups of homotopy spheres I}} | ||
| − | Applied surgery theory to the diffeomorphism classification of smooth structures the n-sphere | + | Applied surgery theory to the diffeomorphism classification of smooth structures on the n-sphere |
|- | |- | ||
|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}} | ||
| + | The topological invariance of the rational Pontrjagin classes. | ||
| + | |- | ||
| + | |1966 || [http://genealogy.math.ndsu.nodak.edu/id.php?id=21659 Brieskorn] || {{citeD2|Brieskorn1966|Beispiele zur Differentialtopologie von Singularitäten}} | ||
|- | |- | ||
|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}} | |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}} | ||
| Line 114: | Line 127: | ||
|1974 || [http://genealogy.math.ndsu.nodak.edu/id.php?id=729 Chapman] || {{citeD2|Chapman1974|Topological invariance of Whitehead torsion}} | |1974 || [http://genealogy.math.ndsu.nodak.edu/id.php?id=729 Chapman] || {{citeD2|Chapman1974|Topological invariance of Whitehead torsion}} | ||
|- | |- | ||
| − | |1977 || [ Kirby] [ Siebenmann] || {{citeD2|Kirby&Siebenmann1977|Foundational essays on topological manifolds, smoothings, and triangulations}} | + | |1977 || [http://en.wikipedia.org/wiki/Robion_Kirby Kirby] [http://en.wikipedia.org/wiki/Larry_Siebenmann Siebenmann] || {{citeD2|Kirby&Siebenmann1977|Foundational essays on topological manifolds, smoothings, and triangulations}} |
|- | |- | ||
| − | |1978 || [ Waldhausen] || {{citeD2|Waldhausen1978|Algebraic $K$-theory of topological spaces I}} | + | |1978 || [http://de.wikipedia.org/wiki/Friedhelm_Waldhausen Waldhausen] || {{citeD2|Waldhausen1978|Algebraic $K$-theory of topological spaces I}} |
|- | |- | ||
| − | |1980 || [ Edwards] || {{citeD2|Edwards1980|The topology of manifolds and cell-like maps}} | + | |1980 || [http://genealogy.math.ndsu.nodak.edu/id.php?id=5408 Edwards] || {{citeD2|Edwards1980|The topology of manifolds and cell-like maps}} |
|} | |} | ||
</wikitex> | </wikitex> | ||
| Line 134: | Line 147: | ||
|1983 || [http://www-history.mcs.st-and.ac.uk/Biographies/Donaldson.html Donaldson] || {{citeD2|Donaldson1983|An application of gauge theory to four-dimensional topology}} | |1983 || [http://www-history.mcs.st-and.ac.uk/Biographies/Donaldson.html Donaldson] || {{citeD2|Donaldson1983|An application of gauge theory to four-dimensional topology}} | ||
|- | |- | ||
| − | |1988 || [ Quinn] || {{citeD2|Quinn1988|Topological transversality holds in all dimensions}} | + | |1988 || [http://en.wikipedia.org/wiki/Frank_Quinn Quinn] || {{citeD2|Quinn1988|Topological transversality holds in all dimensions}} |
|} | |} | ||
</wikitex> | </wikitex> | ||
| Line 144: | Line 157: | ||
! Publication and remarks | ! Publication and remarks | ||
|- | |- | ||
| − | | 1993 || [ Farrell] [ Jones] || {{citeD2|Farrell&Jones1993|Topological rigidity for compact non-positively curved manifolds}} | + | | 1993 || [http://genealogy.math.ndsu.nodak.edu/id.php?id=7649 Farrell] [http://genealogy.math.ndsu.nodak.edu/id.php?id=8429 Jones] || {{citeD2|Farrell&Jones1993|Topological rigidity for compact non-positively curved manifolds}} |
| + | |- | ||
| + | |1996 || [http://en.wikipedia.org/wiki/Andrew_Casson Casson] || {{citeD2|Casson1996|Generalisations and applications of block bundles}} | ||
|} | |} | ||
| Line 156: | Line 171: | ||
|2002 || [http://en.wikipedia.org/wiki/Grigori_Perelman Perelman] || {{citeD2|Perelman2002|The entropy formula for the Ricci flow and its geometric applications}} | |2002 || [http://en.wikipedia.org/wiki/Grigori_Perelman Perelman] || {{citeD2|Perelman2002|The entropy formula for the Ricci flow and its geometric applications}} | ||
|- | |- | ||
| − | |2009 || [ Hill] [Hopkins] [Ravenel] || {{citeD2|Hill&Hopkins&Ravenel2009|On the non-existence of elements of Kervaire invariant one}} | + | |2009 || [http://www.genealogy.ams.org/id.php?id=109370 Hill] [http://en.wikipedia.org/wiki/Michael_J._Hopkins Hopkins] [http://www.math.rochester.edu/people/faculty/doug/Ravenel Ravenel] || {{citeD2|Hill&Hopkins&Ravenel2009|On the non-existence of elements of Kervaire invariant one}} |
|} | |} | ||
</wikitex> | </wikitex> | ||
| − | |||
== Discussion == | == Discussion == | ||
| − | |||
| − | |||
| − | |||
| − | |||
[[Category:History]] | [[Category:History]] | ||
| + | <!-- --> | ||
Latest revision as of 17:06, 18 May 2014
|
The user responsible for this page is Ranicki. No other user may edit this page at present. |
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 |
