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SUMMARY:Helicity\, cohomology\, and configuration spaces - Parsley \, J (W
 ake Forest University\, USA)
DTSTART:20121025T103000Z
DTEND:20121025T113000Z
UID:TALK41165@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We realize helicity as an integral over the compactified confi
 guration space of 2 points on a domain M in R^3. This space is the appropr
 iate domain for integration\, as the traditional helicity integral is impr
 oper along the diagonal MxM. Further\, this configuration space contains a
  two-dimensional cohomology class\, which we show represents helicity and 
 which immediately shows the invariance of helicity under SDiff actions on 
 M. This topological approach also produces a general formula for how much 
 the helicity of a 2-form changes when the form is pushed forward by a diff
 eomorphism of the domain. We classify the helicity-preserving diffeomorphi
 sms on a given domain\, finding new ones on the two-holed solid torus and 
 proving that there are no new ones on the standard solid torus. \n\n(This 
 is joint work with Jason Cantarella.)\n\n
LOCATION:Seminar Room 1\, Newton Institute
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