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5-manifolds: 1-connected

Diarmuid Crowley


We recall the classification of closed smooth simply-connected 5-manifolds begun by Smale in 1962 and completed by Barden in 1965. We also give a construction of every such manifold which differs from Barden's original construction.


5-manifold, smooth manifold, simply connected

Mathematical Subject Classification 2010

Primary: 57R99
Secondary: 57R65


Received: 9th September 2010
Revised: 6th December 2010
Accepted: 30th January 2011
Published: 1st May 2011
Editor: Fuquan Fang