Anelastic attenuation factor: Difference between revisions

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The '''Smale conjecture''', named after [[Stephen Smale]], is the statement that the [[diffeomorphism|diffeomorphism group]] of the [[3-sphere]] has the homotopy-type of its isometry group, the orthogonal group [[orthogonal group|O(4)]].
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== Equivalent statements ==
 
There are several equivalent statements of the Smale conjecture. One is that the component of the unknot in the space of smooth embeddings of the circle in 3-space has the homotopy-type of the round circles, equivalently, [[orthogonal group|O(3)]]. Another equivalent statement is that the group of diffeomorphisms of the [[Ball (mathematics)|3-ball]] which restrict to the identity on the boundary is contractible.
 
== References ==
 
* S.Smale, Diffeomorphisms of the 2-sphere, Proc. AMS 1959.
 
* Hatcher, ''A proof of the Smale conjecture, <math>\scriptstyle{\mathrm {Diff}}(S^{3})\simeq {\mathrm O}(4)</math>.'' Ann. of Math. (2) 117 (1983), no. 3, 553—607.
 
[[Category:Smooth manifolds]]
[[Category:Low dimensional topology]]

Latest revision as of 14:16, 10 November 2014

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