The simplicial EHP sequence in 𝔸1–algebraic topology

Wickelgren, Kirsten¹ ; Williams, Ben²

¹ School of Mathematics, Georgia Institute of Technology, Atlanta, GA, United States
² Department of Mathematics, University of British Columbia, Vancouver, BC, Canada

Geometry & topology, Tome 23 (2019) no. 4, pp. 1691-1777.

Résumé

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

Détail

DOI : 10.2140/gt.2019.23.1691

Classification : 14F42, 19G12, 55Q40
Keywords: $A^1$ homotopy, motivic homotopy, simplicial EHP sequence, motivic homotopy of spheres

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