nLab equivariant weak homotopy equivalence

Idea

In generalization of the notion of weak homotopy equivalences from plain homotopy theory to equivariant homotopy theory, a map of G-spaces is called an equivariant weak homotopy equivalence if it induces isomorphisms on all equivariant homotopy groups.

Related concepts

• equivariant Whitehead theorem

• Elmendorf's theorem

• fine model structure on topological G-spaces

References

See the references at equivariant homotopy group.

Detection in terms of free homotopy sets:

• Takao Matumoto, Norihiko Minami, Masahiro Sugawara, On the set of free homotopy classes and Brown’s construction, Hiroshima Math. J. 14(2): 359-369 (1984) (doi:10.32917/hmj/1206133043)