A comparison of norm maps

We present a spectrum-level version of the norm map in equivariant homotopy theory based on the algebraic construction in work of Greenleess-May. We show that this new norm map is same as the construction in work Hill-Hopkins-Ravenel on the Kervaire invariant problem. Our comparison of the two norm maps gives a conceptual understanding of the choices inherent in the definition of the multiplicative norm map.