Geometry & Topology

The strong Kervaire invariant problem in dimension $62$

Zhouli Xu

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Abstract

Using a Toda bracket computation θ4,2,σ2 due to Daniel C Isaksen, we investigate the 45–stem more thoroughly. We prove that θ42 = 0 using a 4–fold Toda bracket. By work of Barratt, Jones and Mahowald, this implies that θ5 exists and there exists a θ5 such that 2θ5 = 0. Based on θ42 = 0, we simplify significantly their 9–cell complex construction to a 4–cell complex, which leads to another proof that θ5 exists.

Article information

Source
Geom. Topol., Volume 20, Number 3 (2016), 1611-1624.

Dates
Received: 4 November 2014
Accepted: 18 July 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510858998

Digital Object Identifier
doi:10.2140/gt.2016.20.1611

Mathematical Reviews number (MathSciNet)
MR3523064

Zentralblatt MATH identifier
1352.55007

Subjects
Primary: 55Q45: Stable homotopy of spheres

Keywords
Kervaire invariant Toda brackets

Citation

Xu, Zhouli. The strong Kervaire invariant problem in dimension $62$. Geom. Topol. 20 (2016), no. 3, 1611--1624. doi:10.2140/gt.2016.20.1611. https://projecteuclid.org/euclid.gt/1510858998


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