Smooth Field Theories and Homotopy Field Theories
In this thesis we assemble machinery to create a map from the field theories of Stolz and Teichner, which we call smooth field theories, to the field theories of Lurie, which we term homotopy field theories.
Finally, we upgrade this map to work on inner-homs. That is, we provide a map from the fibred category of smooth field theories to the Segal space of homotopy field theories. In particular, along the way we present a definition of symmetric monoidal Segal space, and use this notion to complete the sketch of the defintion of homotopy bordism category employed in Lurie's work to prove the cobordism hypothesis.