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Transactions of the American Mathematical Society

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The Regular Complex in
the $BP\langle 1 \rangle$-Adams Spectral Sequence


Author: Jesús González
Journal: Trans. Amer. Math. Soc. 350 (1998), 2629-2664
MSC (1991): Primary 55T15; Secondary 55P42
DOI: https://doi.org/10.1090/S0002-9947-98-02263-6
MathSciNet review: 1617336
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Abstract: We give a complete description of the quotient complex ${\cal C}$ obtained by dividing out the ${\mathbb F}_{p}$ Eilenberg-Mac Lane wedge summands in the first term of the $BP\langle 1\rangle$-Adams spectral sequence for the sphere spectrum $S^0$. We also give a detailed computation of the cohomology groups $H^{s,t}({\cal C})$ and obtain as a consequence a vanishing line of slope $(p^{2}-p-1)^{-1}$ in their usual $(t-s, s)$ representation. These calculations are interpreted as giving general simple conditions to lift homotopy classes through a $BP\langle 1 \rangle$ resolution of $S^0$.


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Additional Information

Jesús González
Affiliation: Departamento de Matemáticas. Cinvestav. AP 14-740. Mexico DF, Mexico
Email: jesus@math.cinvestav.mx

DOI: https://doi.org/10.1090/S0002-9947-98-02263-6
Keywords: Adams spectral sequence, Adams resolutions, $BP\langle 1 \rangle$ spectrum, Eilenberg-Mac Lane spectrum, cobar complex, weight spectral sequence, vanishing line
Received by editor(s): August 2, 1994
Additional Notes: The author held a fellowship from the Conacyt while this research was performed
Article copyright: © Copyright 1998 American Mathematical Society

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