skip to content

Helicity in differential topology

Presented by: 
Y Mitsumatsu Chuo University
Wednesday 25th July 2012 - 10:10 to 10:30
INI Seminar Room 1
Session Chair: 
Yasuhide Fukumoto
The helicity plays many intresting roles in 3-dimensinal diffential topology. One of its earliest appearences in was the question by Dennis Sullivan, asking to express the Godbilon-Vey invariant in terms 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. If 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 symmetric bilinear form. Some ideas concerning this bilinear form for studies of foliations and contact structures are introduced. For example, in the case of codimmension one foliations the 1st foliated cohomology will appear. If the foliation is deofrmed to contact structures, unexpectedly phenomena which might be related to a quatization procedure is found.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons