## Geometry & Topology

### The chromatic splitting conjecture at $n=p=2$

Agnès Beaudry

#### 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 $πkL1LK(2)V (0)$ is not zero when $k$ is congruent to $− 3$ modulo $8$. We explain how this contradicts the decomposition of $L1LK(2)S$ predicted by the chromatic splitting conjecture.

#### Article information

Source
Geom. Topol., Volume 21, Number 6 (2017), 3213-3230.

Dates
Received: 3 April 2015
Revised: 7 December 2016
Accepted: 19 January 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510859320

Digital Object Identifier
doi:10.2140/gt.2017.21.3213

Mathematical Reviews number (MathSciNet)
MR3692966

Zentralblatt MATH identifier
06779916

#### Citation

Beaudry, Agnès. The chromatic splitting conjecture at $n=p=2$. Geom. Topol. 21 (2017), no. 6, 3213--3230. doi:10.2140/gt.2017.21.3213. https://projecteuclid.org/euclid.gt/1510859320

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