Seminar

Zoom link.

https://msri.zoom.us/s/585445592

Motion groups of links in 3-manifolds arise as a natural generalization of the braid group when passing from (2+1)-TQFTs to (3+1)-TQFTs.  Just as 2D topological phases of matter yield braid group representations by particle exchange, we expect that 3D topological phases of matter give us representations of motion groups.  As the braid group representations coming from (2+1)-TQFTs and braided fusion categories capture quite a bit of the algebraic and topological information (e.g. link invariants and universality of quantum computation models) we could reasonably expect that representations of motion groups would be similarly useful in the (3+1)D setting.  

Having set up this motivation we look at a few examples of motion groups and study their representations. The paucity of explicit representation spaces from (3+1)TQFTs make direct computations difficult.  However, from the results for braid groups we have a few tricks to try--indeed the braid group typically shows up as a subgroup of motions of links so we ask about extending such representations.  I will report on some recent joint work in these directions and discuss some interpretations in line with results on the shortcomings of semisimple (3+1)TQFTs by, for example, Reutter and Qiu-Wang.

Notes 14.5 MB application/pdf

Representations Of Motion Groups