2005/07/08 by Mark Behrens, Behrens, Mark · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Algebraic Topology (math.AT) #Chemical Synthesis and Analysis #FOS: Mathematics #math.AT
paper · pdf · doi:10.48550/arxiv.math/0507182
63 pages, 4 figures, to appear in Trans. AMS
arxiv created 2005/07/08 · openalex publication_date 2005/07/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 E1 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 v1-periodic elements at the prime 3. We also compute the root invariants of some infinite v1-periodic families of elements at the prime 3.