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SUMMARY:Ambidextrous homology theories - Jeremy Hahn (Cambridge)
DTSTART:20250305T160000Z
DTEND:20250305T170000Z
UID:TALK228460@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:Given a homology theory E and an E-orientable manifold M\, the
 re exists a fundamental class in the E homology of M.  Some homology theo
 ries\, including ordinary homology with rational coefficients\, are "ambid
 extrous"---they admit fundamental classes not only for manifolds\, but als
 o manifolds equipped with finite group actions.  I will give a brief intr
 oduction to these ambidextrous theories and then turn to some recent appli
 cations of them.  In particular\, they have been applied by Abouzaid--Blu
 mberg and Abouzaid--McLean--Smith within symplectic topology\, by a number
  of people to the study of etale cohomology in arithmetic geometry\, and t
 o the problem of constructing continuous maps between spheres.
LOCATION:CMS\, MR15
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