Volume 23, issue 4 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
The simplicial EHP sequence in $\mathbb{A}^{1}$–algebraic topology

Kirsten Wickelgren and Ben Williams

Geometry & Topology 23 (2019) 1691–1777
Abstract

We give a tool for understanding simplicial desuspension in A1–algebraic topology: we show that X Ω(S1 X) Ω(S1 X X) is a fiber sequence up to homotopy in 2–localized A1 algebraic topology for X = (S1)m Gmq with m > 1. It follows that there is an EHP spectral sequence

(2) πn+1+iA1 (S2n+2m+1 (G m)2q) (2) πiA1 ,s(Sm (G m)q).

Keywords
$A^1$ homotopy, motivic homotopy, simplicial EHP sequence, motivic homotopy of spheres
Mathematical Subject Classification 2010
Primary: 14F42
Secondary: 19G12, 55Q40
References
Publication
Received: 14 December 2015
Revised: 5 June 2018
Accepted: 11 November 2018
Published: 17 June 2019
Proposed: Jesper Grodal
Seconded: Haynes R Miller, Mark Behrens
Authors
Kirsten Wickelgren
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Ben Williams
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada