EHP spectral sequence
In mathematics, the EHP spectral sequence is a spectral sequence used for inductively calculating the homotopy groups of spheres localized at some prime p. It is described in more detail in and. It is related to the EHP long exact sequence of ; the name "EHP" comes from the fact that George W. Whitehead named 3 of the maps of his sequence "E", "H", and "P".
For the spectral sequence uses some exact sequences associated to the fibration
where stands for a loop space and the is localization of a topological space at the prime 2. This gives a spectral sequence with term equal to
and converging to . The spectral sequence has the advantage that the input is previously calculated homotopy groups. It was used by to calculate the first 31 stable homotopy groups of spheres.
For arbitrary primes one uses some fibrations found by :
where is the -skeleton of the loop space.
