Since their axiomatization by Atiyah in '88, topological field theories (TFTs) have developed into a bridge between topology and representation theory. One goal of my thesis is to give a construction of the 3-manifold invariants coming from an important class of three-dimensional TFTs, namely the Reshetikhin-Turaev construction and its non-semisimple generalization, via the factorization homology of surfaces. In this talk, I will explain the notion of a topological field theory and discuss some important examples in the three-dimensional case. Then I will explain how a consistent system of handlebody group representations (so-called an ansular functor) can be used to obtain a factorization homology description of the semisimple quantum invariants.
