Appears in collection : Mikefest : A conference in honor of Michael Douglas’ 60th birthday

Mathematicians formulate fully extended d-dimensional TQFTs in terms of functors between a higher category of bordism and suitable target categories. Furthermore, the cobordism hypothesis identifies the basic building blocks of such TQFTs. In this talk, I will discuss Rozansky Witten models with affine targets, also known as 3-dimensional topologically twisted N=4 theories of free hypermultiplets. I will show how in this simple example the cobordism hypothesis can be systematically applied to explicitly construct the (infinite-dimensional) state spaces of this theory. Furthermore, a commutative Frobenius algebra will be identified that describes the extended TQFT restricted to circles and bordism between them (Based on work with Nils Carqueville and Daniel Roggenkamp).