Dominik Wrazidlo (Kyushu University) title: Time-interacting fields and actions in positive topological field theories abstract: Positive topological field theories are an axiomatic notion of topological field theory (TFT) over semirings. They have been introduced by M. Banagl to provide a new source of invariants for manifolds of any dimension. Exploiting the concept of Eilenberg completeness for semirings, Banagl has also established a general framework for constructing positive TFTs from systems of fields and category-valued actions on these fields. In this talk, we extend Banagl's framework by conceptualizing notions of time-interacting fields and actions. Thereby, we eliminate all axiomatic drawbacks of Banagl's example of a high dimensional smooth positive TFT that is based on certain fold maps into the plane. Finally, we apply the invariants of the theory to distinguish exotic Kervaire spheres from other exotic spheres.