In this thesis, we calculate the cooperations algebra for the second truncated Brown-Peterson spectrum, BP⟨2⟩, at the prime 2. We accomplish this through the Adams spectral sequence
BP⟨2⟩; F2)) ⇒ BP⟨2⟩* BP⟨2⟩ ⊗ Z2
We begin by introducing a filtration and a splitting of the mod 2 homology of BP⟨2⟩. From this splitting we will derive a splitting on the Ext-groups of BP⟨2⟩
BP⟨2⟩ into a &ugr;2-torsion component, which is concentrated in Adams filtration 0, and a &ugr;2-torsion free component. We then show that this algebraic splitting lifts to a splitting of the spectrum BP⟨2⟩
After establishing our general structural results, we turn to developing an inductive procedure for determining a basis for the &ugr;0-inverted Ext groups of BP⟨2⟩
BP⟨2⟩,and from this determine a F2[&ugr;0]-basis for ExtE(2)*(F2, H*(BP⟨2⟩; F2))= &ugr;0-tors.
|School:||University of Notre Dame|
|School Location:||United States -- Indiana|
|Source:||DAI-B 80/06(E), Dissertation Abstracts International|
|Keywords:||Adams spectral sequence, Brown-peterson spectrum, Cooperations algebra, Margolis homology|
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