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SUMMARY:Helicity in differential topology - Mitsumatsu\, Y (Chuo Universit
 y)
DTSTART:20120725T091000Z
DTEND:20120725T093000Z
UID:TALK39058@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The helicity plays many intresting roles in 3-dimensinal diffe
 ntial topology. One of its earliest appearences in was the question by Den
 nis Sullivan\, asking to express the Godbilon-Vey invariant in terms of li
 nking of fluids. Here the Godbillon-Vey is an invariant for codimension1 f
 oliations which lives in the 3rd de Rham cohomology. The question is well-
 understood and we know which fluid motion should be taken. \n\nIf we think
  of helicity as a quadratic function on the space of incompressible fluids
 \, namely the space of divergence free vector fields\, it goes down to a s
 ymmetric bilinear form. Some ideas concerning this bilinear form for studi
 es of foliations and contact structures are introduced. For example\, in t
 he case of codimmension one foliations the 1st foliated cohomology will ap
 pear. If the foliation is deofrmed to contact structures\, unexpectedly ph
 enomena which might be related to a quatization procedure is found. \n
LOCATION:Seminar Room 1\, Newton Institute
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