Comparison theorems of two Adams spectral sequences (Q1430972)
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scientific article; zbMATH DE number 2068253
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Comparison theorems of two Adams spectral sequences |
scientific article; zbMATH DE number 2068253 |
Statements
Comparison theorems of two Adams spectral sequences (English)
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27 May 2004
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Let \(\lambda: X\to Y\) be a map of ring spectra. For each spectrum \(X\) there are the Adams spectral sequences based on \(E\) and \(F\), \(\{E_r^{s,t}(X)\}\) and \(\{F_r^{s,t}(X)\}\), abutting to \(\pi_{t-s}(X)\) and a morphism of spectral sequences \(\lambda_*:\{E_r^{s,t}(X)\}\to\{F_r^{s,t}(X)\}\) induced by \(\lambda\). Given a map of spectra \(f: X\to Y\) and its induced maps on homotopy \(f_*: \pi_t(X)\to \pi_t(Y)\) with \(t\) an integer, reasonable conditions on these spectral sequences are given which ensure that \(f_*\) is a monomorphism or an epimorphism. Presumably the author has interesting examples in mind but no examples or applications are given.
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Adams spectral sequence
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stable homotopy groups
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