skip to content

Homotopy, link homotopy and (higher?) helicity

Presented by: 
C Shonkwiler University of Georgia
Tuesday 2nd October 2012 - 11:30 to 12:30
INI Seminar Room 1
I will outline a program for relating link homotopy classes of links in Euclidean 3-space to homotopy classes of certain associated maps. This seems worthwhile since interpreting the linking number - which is the simplest link homotopy invariant - as a homotopy invariant leads directly to the famous Gauss linking integral. Indeed, this approach has already yielded a generalized Gauss integral for Milnor's triple linking number.

The overarching goal is to find invariants of vector fields which will be relevant in, e.g., plasma physics. Specifically, these invariants should be "higher" analogues of helicity, meaning invariants of vector fields which are preserved under volume-preserving diffeomorphisms isotopic to the identity and which provide lower bounds for the field energy. Since helicity can be interpreted as an asymptotic version of the Gauss linking integral, the hope is that higher helicities can be defined as asymptotic versions of generalized Gauss integrals for higher linking invariants.
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