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SUMMARY:Cohomology reveals when helicity is a diffeomorphism invariant - P
 arsley\, J (Wake Forest University)
DTSTART:20121206T090000Z
DTEND:20121206T092000Z
UID:TALK41880@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider the helicity of a vector field\, which calculates 
 the average linking number of the fields flowlines. Helicity is invariant 
 under certain diffeomorphisms of its domain  we seek to understand which o
 nes. \n\nExtending to differential (k+1)-forms on domains R^{2k+1}\, we ex
 press helicity as a cohomology class. This topological approach allows us 
 to find a general formula for how much helicity changes when the form is p
 ushed forward by a diffeomorphism of the domain. We classify the helicity-
 preserving diffeomorphisms 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. This approach also leads us to define submanifold helicities:
  differential (k+1)-forms on n-dimensional subdomains of R^m. \n
LOCATION:Seminar Room 1\, Newton Institute
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