Talk:5-manifolds: 1-connected

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1 Conjecture about mapping class groups of 1-connected 5-manifolds

Let M 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))

where B_2(M) is the normal 2-type of M as defined in [Kreck1999]. For example, if M is Spinable with H_2(M) \cong H then

\displaystyle  \Omega_6(B_2(M)) \cong \Omega_6^{Spin}(K(H, 2)).

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 \pi_0\SDiff(M) was computed in [Fang1993] provided that H_2(M) has no 2-torsion and no 3-torsion.~~~~

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