On the unstable Adams spectral sequence for SO and U , and splittings of unstable Ext groups ∗
نویسندگان
چکیده
Let U denote the category of unstable modules over the mod 2 Steenrod algebra A, and let Ext(−) = ExtsU(−,ΣZ2). Let M∞ = H̃∗(ΣCP∞ + ) denote the unstable A-module with nonzero classes xi such that i is odd and positive, and Sqx2k+1 = ( k j ) x2(j+k)+1. Then H∗(U) ≈ U(M∞), where the left side is the mod 2 cohomology of the infinite unitary group, and the right side the free unstable A-algebra generated by M∞. Thus there is an unstable Adams spectral sequence (UASS), defined as in [5], converging to π∗(U) with E s,t 2 ≈ Ext(M∞). We shall construct an algebraic spectral sequence (SS) which we conjecture agrees with this UASS. In Section 3, we perform the minor
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