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spectrum with G-action

Contents

Context

Stable Homotopy theory

Representation theory

Contents

Idea

For GG a topological group, a spectrum with GG-action is a spectrum equipped with an action of GG. In other words, it is a functor from BGBG to the (infinity,1)-category of spectra. The stable homotopy theory of spectra with GG-action is part of the subject of equivariant stable homotopy theory.

Spectra with GG-action are sometimes called “doubly naive” GG-spectra. They are even more naive than naive G-spectra, and can be identified with the full subcategory of G-spectra consisting of “Borel-complete” GG-spectra (see Prop. 6.17 in MNN or Thm. II.2.7 in NS).

See also

References

Last revised on December 19, 2017 at 07:40:03. See the history of this page for a list of all contributions to it.