# 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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