Talk:5-manifolds: 1-connected
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− | The group $\pi_0\SDiff(M)$ was computed in \cite{Fang1993} provided that $H_2(M)$ has no $2$-torsion and no $3$-torsion. | + | The group $\pi_0\SDiff(M)$ was computed in \cite{Fang1993} provided that $H_2(M)$ has no $2$-torsion and no $3$-torsion. |
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Revision as of 15:00, 29 October 2010
1 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
where is the normal -type of as defined in [Kreck1999]. For example, if is Spinable with then
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)
2 Earlier work of Fang
The group was computed in [Fang1993] provided that has no -torsion and no -torsion.