Homology, Homotopy and Applications

Volume 21 (2019)

Number 2

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

Pages: 261 – 278

DOI: https://dx.doi.org/10.4310/HHA.2019.v21.n2.a14


Jocelyne Ishak (School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, United Kingdom)


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.


stable homotopy theory, chromatic homotopy theory

2010 Mathematics Subject Classification


Copyright © 2019, Jocelyne Ishak. Permission to copy for private use granted.

Received 21 November 2018

Accepted 23 November 2018

Published 13 March 2019