Date of Award
Doctor of Philosophy
Part 1 of this work is an application of the Dyer-Lashof Algebra modulo p, an odd prime, to the determination of the Steenrod annihilated indecomposables in the /p homology of the infinite loop space associated to a CW-complex.;Part 2 is concerned with the determination of the algebra struc- ture of K(,*)((OMEGA)('2)S('2n+1); /2) where K(,*)((,-); /2) stands for mod 2, periodic, reduced, complex K-homology theory. Moreover the Atiyah-Hirzebruch spectral sequence for K(,*)((OMEGA)('m)S('n)X; /2) is studied. The main tool in Part 2 are the mod 2 Dyer-Lashof operations acting on finite loop spaces, as well as the Atiyah-Hirzebruch spectral sequence for K-homology.
Mayorquin-garcia, Jesus-manuel, "Homology And K-theory Of Loop Spaces" (1985). Digitized Theses. 1459.