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SUMMARY:Four Manifolds and two complexes with finite fundamental group  - 
 Johnny Nicholson (UCL)
DTSTART:20190301T160000Z
DTEND:20190301T170000Z
UID:TALK119368@talks.cam.ac.uk
CONTACT:Nils Prigge
DESCRIPTION:In this talk\, we will give an overview of various approaches 
 to the classification of non-simply connected 4-manifolds using techniques
  from high-dimensional topology and the algebra of group rings. One approa
 ch is using a modified version of surgery theory\, due to Kreck\, to class
 ify manifolds ‘stably’ up to connected sum with S2 x S2. This leaves u
 s with the ‘unstable’ problem of cancelling the (S2 x S2)-summands\, w
 hich we relate to the corresponding cancellation problems for 2-complexes 
 up to wedging with S2 and Z[pi_1]-modules up to direct sum with a free mod
 ule. We will report on recent progress on these cancellation problems\, an
 d on a related conjecture of C. T. C. Wall from the 1960s.
LOCATION:MR13
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