UCL Mathematical & Physical Sciences


A rose by any other name

A finite energy foliation

20 May 2013

The picture represents a "finite energy foliation" of the 3-dimensional manifold S1 x S2 with its standard contact structure. Finite energy foliations are ways of filling 3-dimensional space with smooth surfaces that are solutions to a differential equation arising in string theory.

Such pictures can help mathematicians gain insight into problems in dynamical systems and in topology - for example, an important strand in research by Chris Wendl (UCL Mathematics) has been using finite energy foliations to try and answer the question, "how many different 4-dimensional shapes could this 3-dimensional shape be the boundary of?

One can use this particular picture to deduce that the answer is exactly one.

Credit: Chris Wendl (UCL Mathematics)