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arXiv:1502.02190 [math.AT]AbstractReferencesReviewsResources

The Chromatic Splitting Conjecture at n=p=2

Agnes Beaudry

Published 2015-02-07Version 1

We show that the strongest form of Hopkins' chromatic splitting conjecture, as stated by Hovey, cannot hold at chromatic level n=2 at the prime p=2. More precisely, for V(0) the mod 2 Moore spectrum, we prove that the k'th homotopy group of L_1L_{K(2)}V(0) is not zero when k is congruent to 5 modulo 8. We explain how this contradicts the decomposition of L_1L_{K(2)}S predicted by the chromatic splitting conjecture.

Categories: math.AT
Subjects: 55Q45, 55P60
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