## A rose by any other name

**20 May 2013**

The picture represents a "finite energy foliation"
of the 3-dimensional manifold *S*^{1} x *S*^{2} 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)

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- This image can be reproduced freely providing the source is credited.

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Page last modified on 20 may 13 09:37

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