Bonn Topology Group - Abstracts

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Talk

January 25, 2022
Sil Linskens (Universität Bonn): Building global stable homotopy theory from equivariant stable homotopy theory

Abstract

Global stable homotopy theory is a formalism which admits applications to orbifold cohomology, elliptic cohomology and importantly for this talk, equivariant stable homotopy theory. Many important equivariant spectra admit natural global refinements, and these refinements have led to theoretical advances and have aided in calculations.

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 stable homotopy theory. For example, the restrictions from global spectra to G-spectra for every compact Lie group G form a conservative family of functors. Nevertheless the precise data encoded by a stable global homotopy type has not yet appeared. I will discuss one way to encode this data, by explaining how global stable homotopy theory can be built up from the G-equivariant stable homotopy theories for compact Lie groups G. Precisely, it is a partially lax limit over all G in the infinity category of infinity categories, lax over the surjections and strict over the injections. (The work presented is joint with Denis Nardin and Luca Pol)

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