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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