Simple description of electromagnetic and gravitational hopfions

General Relativity, Geometry and Analysis: beyond the first 100 years after Einstein

20 November 16:00 - 17:00

Jacek Jezierski - University of Warsaw

A hopfion or Hopf soliton is a `solitonary' solution of spin-N field which has rich topological structure related to Hopf fibration. The Hopf fibration is the simplest non-trivial fibration of three-dimensional sphere. We will study electromagnetic and gravitational solutions based on the Hopf projection which is a surjective map sending great circles on $S^{3}$ to points on $S^{2}$. These circles weave nested toroidal surfaces and each is linked with every other circle exactly once, creating the characteristic Hopf fibration. The characteristic structure of hopfion can be easily seen on the integration curves of the vector field. The structure of closed, linked field lines of hopfions propagates without intersections along the light cone.
Lars Andersson
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Mattias Dahl
KTH Royal Institute of Technology
Philippe G. LeFloch
Sorbonne University
Richard Schoen
University of California, Irvine


Mattias Dahl


For practical matters at the Institute, send an e-mail to