Talk:5-manifolds: 1-connected
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Revision as of 13:47, 7 June 2010 by Diarmuid Crowley (Talk | contribs)
Conjecture about mapping class groups of 1-connected 5-manifolds
Let be a closed, smooth, 1-connected 5-manifold, Matthias Kreck and Diarmuid Crowley conjecture that there is an isomorphism of abelian groups
![\displaystyle \pi_0(\SDiff(M)) \cong \Omega_6(B_2(M))](/images/math/2/3/2/232994b939906872cc750a98faa30f41.png)
where is the normal
-type of
as defined in [Kreck1999]. For example, if
is Spinable with
then
![\displaystyle \Omega_6(B_2(M)) \cong \Omega_6^{Spin}(K(H, 2)).](/images/math/e/8/3/e83aa25a87915092e3244903dee726e4.png)
At present we are checking the details of the proof of this conjecture using the methods of [Kreck1999].
Diarmuid Crowley 10:02, 29 September 2009 (UTC)