This might be a really silly question, but suppose that you have two (possibly Frechet) manifolds M and N both endowed with a G-action. If M and N are homotopy equivalent, is it necessary that they will be G-equivariantly homotopy equivalent?(adsbygoogle = window.adsbygoogle || []).push({});

Edit: That is, should I expect them to have the same equivariant cohomology rings?

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# Equivariant Homotopy

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