Rigidity of the $K(1)$-local stable homotopy category

We investigate a new case of rigidity in stable homotopy theory which is the rigidity of the $K(1)$-local stable homotopy category $\mathrm{Ho} (L_{K(1)} \mathrm{Sp})$ at $p = 2$. In other words, we show that recovering higher homotopy information by just looking at the triangulated structure of $\mathrm{Ho} (L_{K(1)} \mathrm{Sp})$ is possible, which is a property that only a few interesting stable model categories are known to possess.

Keywords

stable homotopy theory, chromatic homotopy theory

2010 Mathematics Subject Classification

55P42

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Received 21 November 2018

Accepted 23 November 2018

Published 13 March 2019