Title : Q-subalgebras, Milnor Basis, and Cohomology
of Eilenberg--Mac Lane Spaces
Author : Hirotaka Tamanoi
Address: Department of Mathematics
University of California Santa Cruz
Santa Cruz, CA 95064, USA
Email: tamanoi@math.ucsc.edu
ABSTRACT. We describe mod $p$ cohomology rings of Eilenberg-Mac Lane
spaces in terms of the Milnor basis rather than in terms of
admissible monomials of the Steenrod algebra. We give a formula of
excess for the Milnor basis elements, correcting Kraines' formula in
odd prime case. Using the Milnor basis description, we study and
characterize certain polynomial subalgebras generated by elements
obtained by applying maximum number of Milnor primitives on mod p
fundamental classes of Eilenberg-Mac Lane spaces. A simple and
interesting unstable pattern emerges. These subalgebras are exact
images of the BP-Thom map into mod p cohomology rings.