Symplectic Cobordism and the Computation of Stable Stems
Seiten
1993
American Mathematical Society (Verlag)
978-0-8218-2558-7 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-2558-7 (ISBN)
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Containing two papers, this title first uses the classical Adams spectral sequence to study the symplectic cobordism ring $/Omega ^*_{Sp}$. It then uses the results of the first paper to analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres.
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.
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.
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.
| Erscheint lt. Verlag | 30.6.1993 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8218-2558-5 / 0821825585 |
| ISBN-13 | 978-0-8218-2558-7 / 9780821825587 |
| Zustand | Neuware |
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