The Weiss derivatives of BO(−) and BU(−)

We study Michael Weiss’ “orthogonal tower” of the functors V↦BO(V) and V↦BU(V). We describe the Weiss derivatives of these functors and calculate the homology of the layers. The orthogonal tower studied here is related to the Goodwillie tower of the identity functor in various ways. Most of our results are Weiss-tower analogues of previous results of Arone–Mahowald and Arone–Dwyer on the Goodwillie derivatives of the identity, but we believe that there are new things to be learned from the Weiss tower.