Decomposition Formula for Milnor's Steenrod Reduced Powers, Mod p Cohomology ofEilenberg-MacLane Spaces in Terms of Milnor Basis, and Q-Subalgebras

摘要

We give a description of the mod p cohomology of Eilenberg-MacLane spaces interms of Milnor basis of the Steenrod algebra defined in terms of its dual algebra. In this description, the admissibility condition is automatically satisfied and the unstable excess condition assumes a very simple form. We characterize their polynomial Q-subalgebras generated by elements obtained by applying maximum number of Milnor primitives to the mod p fundamental classes for Eilenberg-MacLane spaces. The main ingredients are decomposition formulae for Milnor's Steenrod reduced powers and Steenrod squares in a form suitable for unstable application.