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

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#REDIRECT [[Talk:5-manifolds: 1-connected/ 1st edition]]
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== Conjecture about mapping class groups of 1-connected 5-manifolds ==
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<wikitex>;
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Let $M$ be a closed, smooth, 1-connected 5-manifold, [[User:Matthias Kreck|Matthias Kreck]] and [[User:Diarmuid Crowley|Diarmuid Crowley]] conjecture that there is an isomorphism of abelian groups
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$$ \pi_0(\SDiff(M)) \cong \Omega_6(B_2(M)) $$
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where $B_2(M)$ is the normal $2$-type of $M$ as defined in {{cite|Kreck1999}}. For example, if $M$ is Spinable with $H_2(M) \cong H$ then
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$$ \Omega_6(B_2(M)) \cong \Omega_6^{Spin}(K(H, 2)).$$
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At present we are checking the details of the proof of this conjecture using the methods of {{cite|Kreck1999}}.
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</wikitex>
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[[User:Diarmuid Crowley|Diarmuid Crowley]] 10:02, 29 September 2009 (UTC)

Latest revision as of 11:59, 17 August 2010

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

Let
Tex syntax error
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
Tex syntax error
as defined in [Kreck1999]. For example, if
Tex syntax error
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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