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2016 The strong Kervaire invariant problem in dimension $62$
Zhouli Xu
Geom. Topol. 20(3): 1611-1624 (2016). DOI: 10.2140/gt.2016.20.1611

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.

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Zhouli Xu. "The strong Kervaire invariant problem in dimension $62$." Geom. Topol. 20 (3) 1611 - 1624, 2016. https://doi.org/10.2140/gt.2016.20.1611

Information

Received: 4 November 2014; Accepted: 18 July 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1352.55007
MathSciNet: MR3523064
Digital Object Identifier: 10.2140/gt.2016.20.1611

Subjects:
Primary: 55Q45

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.20 • No. 3 • 2016
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