Talk:5-manifolds: 1-connected/1st edition

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[edit] Conjecture about mapping class groups of 1-connected 5-manifolds

Let M/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_lj9Weu 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)

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