2014/07/13 by Donald M. Larson, Larson, Donald M.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT
paper · pdf · doi:10.48550/arxiv.1407.3423
Several important corrections and improvements made, especially in the introduction and in Section 7
arxiv created 2015/03/23 · arxiv updated 2015/03/24
We compute the Adams-Novikov E2-term of a spectrum Q(2) constructed by Behrens. The homotopy groups of Q(2) are closely tied to the 3-primary stable homotopy groups of spheres; in particular, they are conjectured to detect the homotopy beta family of Greek letter elements at the prime 3. Our computation leverages techniques used by Behrens to compute the rational homotopy of Q(2), and leads to a conjecture that the Adams-Novikov E2-term for Q(2) detects the algebraic beta family in the BP-based Adams-Novikov E2-term for the 3-local sphere.