Talk:5-manifolds: 1-connected
From Manifold Atlas
Revision as of 19:05, 16 December 2010 by Diarmuid Crowley (Talk | contribs)
[edit] 1 Conjecture about mapping class groups of 1-connected 5-manifolds
Tex syntax errorbe a closed, smooth, 1-connected 5-manifold, Matthias Kreck and Diarmuid Crowley conjecture that there is an isomorphism of abelian groups



Tex syntax erroras defined in [Kreck1999]. For example, if
Tex syntax erroris Spinable with


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)
[edit] 2 Earlier work of Fang
The group was computed in [Fang1993] provided that
has no
-torsion and no
-torsion.
[edit] Up-date of conjecture: module structure
If the conjecture above holds, then from the short exact sequence

we obtain an action of on the abelian group
. Diarmuid Crowley and Matthias Kreck also conjecture that the action of
is via the induced action on
. In particular, if
is spinable with
, then
acts on
in the obvious way and so on
.