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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Helicity in differential topology - Mitsumatsu\, Y
(Chuo University)
DTSTART;TZID=Europe/London:20120725T101000
DTEND;TZID=Europe/London:20120725T103000
UID:TALK39058AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39058
DESCRIPTION:The helicity plays many intresting roles in 3-dime
nsinal diffential topology. One of its earliest ap
pearences in was the question by Dennis Sullivan\,
asking to express the Godbilon-Vey invariant in t
erms of linking of fluids. Here the Godbillon-Vey
is an invariant for codimension1 foliations 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 vecto
r fields\, it goes down to a symmetric bilinear fo
rm. Some ideas concerning this bilinear form for s
tudies of foliations and contact structures are in
troduced. For example\, in the case of codimmensio
n one foliations the 1st foliated cohomology will
appear. If the foliation is deofrmed to contact st
ructures\, unexpectedly phenomena which might be r
elated to a quatization procedure is found. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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