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ISSN 1088-6850(e) ISSN 0002-9947(p)

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
Posted: August 1, 2005
MathSciNet review: 2231379
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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a ring spectrum for which the -Adams spectral sequence converges. We define a variant of Mahowald's root invariant called the `filtered root invariant' which takes values in the term of the -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 -Adams spectral sequence. These theorems are compared to some known computations of root invariants at the prime . We use the filtered root invariants to compute some low-dimensional root invariants of -periodic elements at the prime . We also compute the root invariants of some infinite -periodic families of elements at the prime .

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