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SUMMARY:An overview of the classification of simply-connected 7-manifolds 
 [MPIM]
DTSTART:20260928T110000Z
DTEND:20260928T130000Z
DTSTAMP:20260926T014400Z
UID:indico-event-1599@math-events.uni-bonn.de
DESCRIPTION:Speakers: Diarmuid Crowley (University of Melbourne)\n\nMPIM T
 opology Seminar\nI will present a program to classify closed\, simply-conn
 ected\, spin 7-manifolds M.  The classification is organised by the group
 s H_2(M) and H_3(M)\,  Due to the work of Kreck\, Kreck-Stolz\, Hepworth 
 much is know about the case where A is torsion free.\nIt is helpful to fir
 st classify "polarised manifolds"\, where an isomorphism H_2(M) \\to A is
  added to the data.  Setting H_3(M) = 0\, we obtain a set of “sphere-li
 ke” manifolds\, which we call “Theta-manifolds”\, and taking the su
 bset of polarised “Theta-manifolds” which spin bound over the Eilenb
 erg-MacLane space K(A\, 2)\, we obtain the group bspin_8(A). \nOur progra
 m has 4 mains steps: compute the group bspin_8(A)\, prove that it acts on 
 sets isomorphism classes of polarised manifolds\, identify invariants whic
 h classify the orbit of this action\, and finally show how to compute the 
 stabiliser of each orbit.\nThis is part of a joint project with Johannes N
 ordström\, and includes joint work with Csaba Nagy.\n \n\nhttps://math-e
 vents.uni-bonn.de/event/1599/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1599/
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