A Generalization of the Atiyah–Hirzebruch Spectral Sequence

Exactness of homotopy functors of spaces

“…In [13], Hakim-Hashemi and Kahn study the GAHSS, and identify the E 2 term in the event that F is homotopy exact, which will be defined below. They also introduce a criterion on F for determining when the spectral sequence collapses.…”

“…Unfortunately, the difficulties seen in extending the work of [13] lead to the conclusion that the filtration of the spectral sequence is too coarse to be useful, and another path must be taken to obtain further progress. The author has derived a more tractable spectral sequence containing similar information which will be studied in a future article.…”

“…The major result of [13] involving homotopy exact functors was Theorem 1.4. If F is a homotopy exact functor, then given any generalized homology theory E * , E * • F is itself a generalized homology theory.…”