The Chromatic Splitting Conjecture at n=p=2
Algebraic Topology
2018-03-16 v3
Abstract
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 kth homotopy group of L_1L_{K(2)}V(0) is not zero when k is congruent to -3 modulo 8. We explain how this contradicts the decomposition of L_1L_{K(2)}S predicted by the chromatic splitting conjecture.
Cite
@article{arxiv.1502.02190,
title = {The Chromatic Splitting Conjecture at n=p=2},
author = {Agnes Beaudry},
journal= {arXiv preprint arXiv:1502.02190},
year = {2018}
}
Comments
Revised version. To appear in Geometry & Topology