Quantum topology offers tools to construct topological
invariants of knots and 3-manifolds, that are computable with simple
exponential algorithms. On the one hand, we are given algebraic data (a
fusion category) and on the other hand a topological object (we will
focus on 3-manifolds presented by triangulations). In this talk, I will
review the construction of 3-manifold quantum invariants and give an
overview of their computational complexity, depending on both the fusion
category and the input triangulated 3-manifold. I will also illustrate
general strategies for fast computation.
