The Equivariant Generating Hypothesis
by Anna Marie Bohmann
Abstract: Freyd's generating hypothesis is a long-standing conjecture in stable homotopy theory. The conjecture says that if a stable map between finite CW-complexes induces the zero map on stable homotopy groups, then it must actually be stably nullhomotopic. We formulate the appropriate version of this conjecture in the equivariant setting, beginning with a brief discussion of equivariant homotopy groups. 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 \(S^1\).