By Stanley O. Kochman

This booklet includes self sufficient but similar papers. within the first, Kochman makes use of the classical Adams spectral series to review the symplectic cobordism ring $\Omega ^*_{Sp}$. Computing better differentials, he indicates that the Adams spectral series doesn't cave in. those computations are utilized to check the Hurewicz homomorphism, a dead ringer for $\Omega ^*_{Sp}$ within the unoriented cobordism ring, and identical to the strong homotopy teams of spheres in $\Omega ^*_{Sp}$. The constitution of $\Omega ^{-N}_{Sp}$ is decided for $N\leq 100$. within the moment paper, Kochman makes use of the result of the 1st paper to investigate the symplectic Adams-Novikov spectral series converging to the solid homotopy teams of spheres. He makes use of a generalized lambda algebra to compute the $E_2$-term and to investigate this spectral series via measure 33.

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**Example text**

Thus, 0 is a monomorphism. (b) Let ( : BSp —» £ [ / and f : MSp -* M [ / be the canonical maps. Recall that C# : H*BSp —» HmBU is a monomorphism with torsion-free cokernel. Thus, (Tf)# = £# : H+MSp —> H+MU is a monomorphism with torsion-free cokernel. Consider the following commutative diagram: MSp, ^ - M£/. 2), it is clear that H£m [hlVa,b] is divisible by 4, H£m [h0V2n] is divisible by 2 and H£m[Q(n)] is divisible by 8. Thus, H [hlVa,b] is divisible by 4, H [h0V2n] is divisible by 2 and H[Q(n)] is divisible by 8.

In Section 5, we generalize the Second Reduction Theorem of [13] to construct Aj p as a quotient of 5- We show that A*Sp splits into a direct sum of subcomplexes, one subcomplex for each group generator of the M5p*A/5p-primitive elements of MSpm. In our range of computation, these elements are 1, $1^3 G MSp^\ and rfcat G MSpst+c+i for t > 0 and e = 0,1. In Section 6, we use a Bockstein spectral sequence to compute the homology of T*Spy the direct summand of A J corresponding to 1 determined by A/Sp*/Torsion.

4 ^ 2 + *4S(0,1,4)V 6 . (h) £ = $4*5 V& + *»Vft + * , * , ! & + *JV W . / / E i E 2 =