This book contains two independent yet related papers. In the first, Kochman uses the classical Adams spectral sequence to study the symplectic cobordism ring $\Omega ^*_{Sp}$. Computing higher differentials, he shows that the Adams spectral sequence does not collapse. These computations are applied to study the Hurewicz homomorphism, the image of $\Omega ^*_{Sp}$ in the unoriented cobordism ring, and the image of the stable homotopy groups of spheres in $\Omega ^*_{Sp}$. The structure of $\Omega ^{-N}_{Sp}$ is determined for $N\leq 100$. In the second paper, Kochman uses the results of the first paper to analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres. He uses a generalized lambda algebra to compute the $E_2$-term and to analyze this spectral sequence through degree 33.
Reihe
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Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Maße
Höhe: 255 mm
Breite: 180 mm
ISBN-13
978-0-8218-2558-7 (9780821825587)
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Schweitzer Klassifikation
The symplectic cobordism ring III Introduction Higher differentials-theory Higher differentials-examples The Hurewicz homomorphism The spectrum msp The image of $\Omega ^\last _{Sp}$ in ${\mathfrak N} ^\ast$ On the image of $\pi ^S_\ast$ in $\Omega ^\ast _{Sp}$ The first hundred stems The symplectic Adams Novikov spectral sequence for spheres Introduction Structure of $MSp_\ast$ Construction of $\Lambda ^\ast _{Sp}$ -The first reduction theorem Admissibility relations Construction of $\Lambda ^\ast _{Sp}$ -The second reduction theorem Homology of $\Gamma ^\ast _{Sp}$ -The Bockstein spectral sequence Homology of $\Lambda [\alpha _t]$ and $\Lambda [\eta\alpha _t]$ The Adams-Novikov spectral sequence Bibliography.
