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arXiv · 1710.08018

Inverting the Hopf map

Michael Andrews·Haynes Miller
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Abstract

We calculate the $\eta$-localization of the motivic stable homotopy ring over the complex numbers, confirming a conjecture of Guillou and Isaksen. Our approach is via the motivic Adams-Novikov spectral sequence. In fact, work of Hu, Kriz, and Ormsby implies that it suffices to compute the corresponding localization of the classical Adams-Novikov $E_2$-term, and this is what we do. Guillou and Isaksen also proposed a pattern of differentials in the localized motivic classical Adams spectral sequence, which we verify using a method first explored by Novikov.

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Michael Andrews, Haynes Miller. 2017-10-22. Inverting the Hopf map. https://arxiv.org/abs/1710.08018

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