# The Equivariant Generating Hypothesis

Algebra/Geometry/Topology Seminar

#### by Anna Marie Bohmann

Institution: Northwestern University
Date: Fri 7th September 2012
Time: 3:15 PM
Location: 213 Richard Berry

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 $$S^1$$.