Freyd's generating hypothesis is a long-standing conjecture in stable homotopy theory. The conjecture says that if a map between finite spectra induces the zero map on homotopy groups, then it must actually be nullhomotopic. We formulate the appropriate version of this conjecture in the equivariant setting. We then give some results about this equivariant version and compare them to the nonequivariant results. In particular, we show that the rational version of this conjecture holds when the group of equivariance is finite, but fails when the group is S^1.

For more information, contact Khalid Bou-Rabee khalidb[at]umich(dot)edu