Memoirs of the American Mathematical Society 2012; 90 pp; softcover Volume: 218 ISBN10: 0821869027 ISBN13: 9780821869024 List Price: US$67 Individual Members: US$40.20 Institutional Members: US$53.60 Order Code: MEMO/218/1026
 The author studies the interaction between the EHP sequence and the Goodwillie tower of the identity evaluated at spheres at the prime \(2\). Both give rise to spectral sequences (the EHP spectral sequence and the Goodwillie spectral sequence, respectively) which compute the unstable homotopy groups of spheres. He relates the Goodwillie filtration to the \(P\) map, and the Goodwillie differentials to the \(H\) map. Furthermore, he studies an iterated AtiyahHirzebruch spectral sequence approach to the homotopy of the layers of the Goodwillie tower of the identity on spheres. He shows that differentials in these spectral sequences give rise to differentials in the EHP spectral sequence. He uses his theory to recompute the \(2\)primary unstable stems through the Toda range (up to the \(19\)stem). He also studies the homological behavior of the interaction between the EHP sequence and the Goodwillie tower of the identity. This homological analysis involves the introduction of DyerLashoflike operations associated to M. Ching's operad structure on the derivatives of the identity. These operations act on the mod \(2\) stable homology of the Goodwillie layers of any functor from spaces to spaces. Table of Contents  Introduction
 DyerLashof operations and the identity functor
 The Goodwillie tower of the EHP sequence
 Goodwillie filtration and the \(P\) map
 Goodwillie differentials and Hopf invariants
 EHPSS differentials
 Calculations in the \(2\)primary Toda range
 Appendix A. Transfinite spectral sequences associated to towers
 Bibliography
