In
geometric topology, the double suspension theorem of
James W. Cannon () and Robert D. Edwards states that the double
suspension
Suspension or suspended may refer to:
Science and engineering
* Suspension (topology), in mathematics
* Suspension (dynamical systems), in mathematics
* Suspension of a ring, in mathematics
* Suspension (chemistry), small solid particles suspende ...
''S''
2''X'' of a
homology sphere ''X'' is a topological sphere.
[James W. Cannon, "Σ2 H3 = S5 / G", ''Rocky Mountain J. Math.'' (1978) 8, pp. 527-532.]
If ''X'' is a
piecewise-linear homology sphere but not a sphere, then its double suspension ''S''
2''X'' (with a triangulation derived by applying the double suspension operation to a triangulation of ''X'') is an example of a triangulation of a topological sphere that is not piecewise-linear. The reason is that, unlike in piecewise-linear manifolds, the link of one of the suspension points is not a sphere.
See also
*
References
*
*{{Citation , last1=Latour , first1=François , title=Séminaire Bourbaki vol. 1977/78 Exposés 507–524 , publisher=
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
Originally founded in 1842 ...
, location=Berlin, New York , language=French , series=Lecture Notes in Math. , isbn=978-3-540-09243-8 , doi=10.1007/BFb0069978 , mr=554220 , year=1979 , volume=710 , chapter=Double suspension d'une sphère d'homologie
'après R. Edwards, pages=169–186
* Steve Ferry
Geometric Topology Notes(''See Chapter 26, page 166'')
Geometric topology
Theorems in topology