Download Symplectic Cobordism and the Computation of Stable Stems by Stanley O. Kochman PDF

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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Extra info for Symplectic Cobordism and the Computation of Stable Stems

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) £ =$4*5 V& + *»Vft + * , * , ! & + *JV W . / / E i E 2 = 3; (v) i / E * = * £ [ ^ V ^ , + *,Vg B ] m. , e, / ) 2/ien a ^ mz'n {a, d, e, / } . (b) 3>a$fcEiE2 where 1 < a < 6 ana* Ei, E2 are /wo distinct elements listed in (1) such that: (i) Ei ±$ c anc? E 2 ^ $c ; (ii) f / ^ a$ 6 E 1 E 2 = *\ [\$iV 4e+ 2 + ^ V g J E then e >