There is a close relationship between derived loop spaces, a geometric object, and Hochschild homology, a categorical invariant, made possible by derived algebraic geometry, thus allowing for both intuitive insights and new computational tools. In the case of a quotient stack, we discuss a "Jordan decomposition" of loops which is made precise by an equivariant localization result. We also discuss an Atiyah-Segal completion theorem which relates completed periodic cyclic homology to Betti cohomology.
- Mathematical physics
- Scientific Series