# A theorem on multiplicative cell attachments with an application to Ravenel’s X(n) spectra

@article{Beardsley2017ATO,
title={A theorem on multiplicative cell attachments with an application to Ravenel’s X(n) spectra},
author={Jonathan Beardsley},
journal={Journal of Homotopy and Related Structures},
year={2017},
pages={1-14}
}
We show that the homotopy groups of a connective $$\mathbb {E}_k$$Ek-ring spectrum with an $$\mathbb {E}_k$$Ek-cell attached along a class $$\alpha$$α in degree n are isomorphic to the homotopy groups of the cofiber of the self-map associated to $$\alpha$$α through degree 2n. Using this, we prove that the $$2n-1$$2n-1st homotopy groups of Ravenel’s X(n) spectra are cyclic for all n. This further implies that, after localizing at a prime, $$X(n+1)$$X(n+1) is homotopically unique as the… Expand
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