The simplicial EHP sequence in 𝔸1–algebraic topology

Wickelgren, Kirsten; Williams, Ben

doi:10.2140/gt.2019.23.1691

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

The simplicial EHP sequence in $\mathbb{A}^{1}$–algebraic topology

Kirsten Wickelgren and Ben Williams

Geometry & Topology 23 (2019) 1691–1777

DOI: 10.2140/gt.2019.23.1691

Abstract

We give a tool for understanding simplicial desuspension in $A^{1}$ –algebraic topology: we show that $X \to Ω (S^{1} \land X) \to Ω (S^{1} \land X \land X)$ is a fiber sequence up to homotopy in $2$ –localized $A^{1}$ algebraic topology for $X = {(S^{1})}^{m} \land G_{m}^{\land q}$ with $m > 1$ . It follows that there is an EHP spectral sequence

ℤ_{(2)} \otimes π_{n + 1 + i}^{A^{1}} (S^{2 n + 2 m + 1} \land {(G_{m})}^{\land 2 q}) \Rightarrow ℤ_{(2)} \otimes π_{i}^{A^{1}, s} (S^{m} \land {(G_{m})}^{\land q}) .

PDF Access Denied

We have not been able to recognize your IP address 3.134.81.206 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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

Volume 23, issue 4 (2019)