A Generalization of the Atiyah–Hirzebruch Spectral Sequence

Hakim-Hashemi, Mehdi
Kahn, Donald W.

¹School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A. and Department of Mathematics, College of Arts and Sciences, Shiriz, Iran
²School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A. e-mail: [email protected]

K-Theory 11(3):p 241-257, April 1997.

The classical Atiyah-Hirzebruch spectral sequence relates the ordinary homology with coefficients in h*(*) to h*(-). We study a spectral sequence converging to h(F(-)) where F is a (reasonable) functor on spaces. We determine precisely when this spectral sequence collapses and we develop the basic elementary theory of such functors. When F is a reduced homotopy exact functor, H(F(-)) is a homology theory and this reduces to the classical case of Atiyah-Hirzebruch. We calculate various examples to show that the theory is nontrivial.