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

From Manifold Atlas

## [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)