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

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< Talk:5-manifolds: 1-connected(Difference between revisions)

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− | + | == Conjecture about mapping class groups of 1-connected 5-manifolds == | |

+ | <wikitex>; | ||

+ | 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 | ||

+ | $$ \pi_0(\SDiff(M)) \cong \Omega_6(B_2(M)) $$ | ||

+ | 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 | ||

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

+ | At present we are checking the details of the proof of this conjecture using the methods of {{cite|Kreck1999}}. | ||

+ | </wikitex> | ||

+ | |||

+ | [[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 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)