A-homology, A-homotopy and spectral sequences

Enzo Miguel Ottina

Given a CW-complex $A$ we define an `$A$-shaped' homology theory which behaves nicely towards $A$-homotopy groups allowing the generalization of many classical results. We also develop a relative version of the Federer spectral sequence for computing $A$-homotopy groups. As an application we derive a generalization of the Hopf-Whitney theorem.

Journal of Homotopy and Related Structures, Vol. 6(2011), No. 1, pp. 161-173