Speaker: Sil Linskens - University of Bonn
Abstract: Global equivariant stable homotopy theory is a formalism which admits applications to orbifold cohomology, elliptic cohomology and importantly equivariant stable homotopy theory. Many important equivariant spectra admit global refinements, and these refinements have led to theoretical advances and have aided in calculations. However not only does global homotopy theory admit applications to equivariant homotopy theory, but it seems reasonable to expect that global homotopy theory is in some sense determined by equivariant homotopy theory. For example, there exists a restriction functor which sends a global spectrum to a $G$-spectrum for every compact Lie group $G$. Furthermore, these collectively form a conservative family of functors. I will present a result which explains exactly how the infinity category of global spectra is built from the infinity categories of $G$-spectra. It says that the infinity category of global spectra is a partially lax limit of a diagram indexing the infinity categories of $G$-spectra for all $G$, lax on the surjections and strict on the injections. (The work presented is joint with Denis Nardin and Luca Pol).