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SUMMARY:Tight but nonfillable contact manifolds in all dimensions - Chris 
 Wendl\, UCL
DTSTART:20111130T160000Z
DTEND:20111130T170000Z
UID:TALK34611@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:Contact topology in dimension three is shaped by the fundament
 al dichotomy between "tight" and "overtwisted" contact structures\, and wh
 ile it is not known whether any such dichotomy exists in higher dimensions
 \, there are certainly contact structures in all dimensions\nthat have all
  the trappings of overtwistedness (e.g. nonfillability\, vanishing contact
  homology)\, or tightness (e.g. admitting a Reeb vector field with no cont
 ractible orbits).  In dimension 3\, the\ninvariant known as "Giroux torsio
 n" has played a central role in classifying tight contact structures\, and
  in this talk I will explain how one can generalize it to find the first e
 xamples in all dimensions\nof contact structures that must be considered t
 ight but do not admit any symplectic fillings.  A crucial ingredient for t
 his is the existence (also in all dimensions) of symplectic manifolds with
 \ndisconnected convex boundary\, which requires a surprising digression in
 to algebraic number theory.  This is joint work with Patrick Massot and Kl
 aus Niederkrueger.
LOCATION:MR13
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