Actions of the circle group on presentable stable infinity-categories

Abstract

This dissertation seeks to identify actions by the circle group on presentable stable infinity- categories. A circle action on the category of chain complexes over a commutative ring is equivalent with the data of a degree 1 differential map. In the more generalized setting, this characterization of a circle group action is obstructed precisely by the Hopf fibration. This is identified using the theory of stratifications.