Symplectic Cobordism and the Computation of Stable Stems (Memoirs of the American Mathematical Society)

Symplectic Cobordism and the Computation of Stable Stems (Memoirs of the American Mathematical Society)

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Description

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.

Contents

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.

Product Details

  • ISBN13: 9780821825587
  • Format: Paperback
  • Number Of Pages: 88
  • ID: 9780821825587
  • ISBN10: 0821825585

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