On the fate of $η^3$ in higher analogues of Real bordism

Michael A. Hill

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arXiv · 1507.08083

On the fate of $η^3$ in higher analogues of Real bordism

Michael A. Hill

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Abstract

We show that the cube of the Hopf map $η$ maps to zero under the Hurewicz map for all fixed points of all norms to cyclic $2$-groups of the Landweber-Araki Real bordism spectrum. Using that the slice spectral sequence is a spectral sequence of Mackey functors, we compute the relevant portion of the homotopy groups of these fixed points, showing that multiplication by $4$ annihilates $π_{3}$.

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Michael A. Hill. 2015-07-29. On the fate of $η^3$ in higher analogues of Real bordism. https://arxiv.org/abs/1507.08083

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