Volume 8, issue 3 (2008)

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The $5$–local homotopy of $eo_4$

Michael A Hill

Algebraic & Geometric Topology 8 (2008) 1741–1761
Abstract

We compute the cohomology of a $5$–local analogue of the Weierstrass Hopf algebroid used to compute $tmf$–homology. We also compute the Adams–Novikov differentials for various stages, finding the homotopy, $V\left(0\right)$–homology and $V\left(1\right)$–homology of the putative spectrum $e{o}_{4}$. We also link this computation to the homotopy of the higher real $K$–theory spectrum $E{O}_{4}$.

Keywords
Bockstein, K-theory, Hopkins–Miller
Mathematical Subject Classification 2000
Primary: 55T25, 18G40, 55N35
Secondary: 55Q51, 18G60