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Title：Almost global homotopy theory Speaker：Hun Zhen郇真（中山大学）Time：2018.9.25，3-5pmLocation: Center for Mathematical Sciences, Room 813Abstract：Many important equivariant theories naturally exist not only for a particular group, but in a uniform way for a family of groups. Prominent examples are equivariant stable homotopy theory, equivariant K-theory and equivariant bordism. This ...

Title：Almost global homotopy theory

Speaker：Huan Zhen郇真（中山大学）

Time：2018.9.25，3-5pm

Location: Center for Mathematical Sciences, Room 813

Abstract：

Many important equivariant theories naturally exist not only for a particular group, but in a uniform way for a family of groups. Prominent examples are equivariant stable homotopy theory, equivariant K-theory and equivariant bordism. This observation led to the birth of global homotopy theory. Globalness is a measure of the naturalness of a cohomology theory. Schwede developed a modern approach of it by global orthogonal spectra, which is inspired by Greenlees and May.

So far several models of global homotopy theory have been established with different motivations and advantages, including Bohmann's model, Gepner's model and Rezk's model. We construct a new global homotopy theory, almost global homotopy theory, which is equivalent to the previous models. But with it we can show that quasi-theories can be globalized if the original cohomology theory can be globalized. This leads to the conjecture that the globalness of a cohomology theory is determined by the formal component of its divisible group; when the etale component varies, the globalness does not change.