Root invariants in the Adams spectral sequence

Details Root invariants in the Adams spectral sequence Root invariants in the Adams spectral sequence

2005-07-08

arxiv.org/abs/math/0507182v1

Mathematics

Algebraic Topology

63 pages, 4 figures, to appear in Trans. AMS

Scientific paper

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 concern 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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