Loops in Leeds:

Motion groups and related topics

1 - 4 July 2019

School of Mathematics, University of Leeds

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This workshop will revolve around loop braid groups and related braided and knotted structures, throughout different areas of geometric topology, with an eye on applications in physics, namely modelling topological phases of matter.

Loop braid groups admit many equivalent formalisms: they can be seen as motion groups of circles in a 3-dimensional space, but also also as groups of basis-conjugating automorphisms of the free groups, as fundamental groups of the configuration spaces of circles, and topologically, as embeddings in a 4-dimensional space of disjoint copies of the oriented annulus with fixed boundary components. They also have a combinatorial interpretation as as welded braids diagrams.

In this framework, the purpose of the workshop is the following:

1. Recognising the breadth of the role of loop braid groups, and motion groups in general, in low dimensional topology, models of topological phases of matter, and representation theory;

2. Identifying common problems that allow for multiple phrasings and approaches, that could complement one another;

3. Encouraging interaction between experts in different domains, by bringing together and promoting communication between experts across disciplines in which loop braid groups, motion groups and related knotted objects play a role.

We gratefully acknowledge funding from Leeds University School of Mathematics, and the London Mathematical Society.

This workshops sits in the framework of the Leverhulme Trust Research Project : Emerging Physics From Lattice Models of Higher Gauge Theory.