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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The strong Kervaire invariant problem in dimension $62$

Zhouli Xu

Geometry & Topology 20 (2016) 1611–1624
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.

Keywords
Kervaire invariant, Toda brackets
Mathematical Subject Classification 2010
Primary: 55Q45
References
Publication
Received: 4 November 2014
Accepted: 18 July 2015
Published: 4 July 2016
Proposed: Paul Goerss
Seconded: Haynes Miller, Ronald Stern
Authors
Zhouli Xu
Department of Mathematics
University of Chicago
5734 S. University Avenue, Room 208C
Chicago, IL 60637
USA