Quantum representations of handlebody groups

Lukas Mueller, Perimeter Institute for Theoretical Physics

Mapping class groups of surfaces and handlebody groups are fundamental objects in low-dimensional topology.  Quantum algebra and mathematical physics provide large classes of finite dimensional representations for both.

In this talk, I will discuss examples of those representations and their properties. An important feature is that they are local under cutting and gluing of handlebodies. I will sketch an approach to a precise formulation of this property and present a complete classification result. The talk is based on joint work with Lukas Woike.

QNC 2501