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Root invariants in the Adams spectral sequence


Author: Mark Behrens
Journal: Trans. Amer. Math. Soc. 358 (2006), 4279-4341
MSC (2000): Primary 55Q45; Secondary 55Q51, 55T15
DOI: https://doi.org/10.1090/S0002-9947-05-03773-6
Published electronically: August 1, 2005
MathSciNet review: 2231379
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Abstract: Let $E$ be a ring spectrum for which the $E$-Adams spectral sequence converges. We define a variant of Mahowald's root invariant called the `filtered root invariant' which takes values in the $E_1$ term of the $E$-Adams spectral sequence. The main theorems of this paper are concerned with when these filtered root invariants detect the actual root invariant, and explain a relationship between filtered root invariants and differentials and compositions in the $E$-Adams spectral sequence. These theorems are compared to some known computations of root invariants at the prime $2$. We use the filtered root invariants to compute some low-dimensional root invariants of $v_1$-periodic elements at the prime $3$. We also compute the root invariants of some infinite $v_1$-periodic families of elements at the prime $3$.


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Additional Information

Mark Behrens
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

DOI: https://doi.org/10.1090/S0002-9947-05-03773-6
Received by editor(s): November 4, 2003
Received by editor(s) in revised form: June 16, 2004
Published electronically: August 1, 2005
Additional Notes: The author was partially supported by the NSF
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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