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arXiv · 1411.5306

The Simplicial EHP Sequence in A1-Algebraic Topology

Kirsten Wickelgren·Ben Williams
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Abstract

We give a tool for understanding simplicial desuspension in A1-algebraic topology: we show that $X \to Ω(S^1 \wedge X)\to Ω(S^1 \wedge X \wedge X)$ is a fiber sequence up to homotopy in 2-localized A1-algebraic topology for $X = (S^1)^m \wedge G_m^{\wedge q}$ with $m>1$. It follows that there is an EHP sequence spectral sequence $$Z_{(2)} \otimes π_{n+1+i}^{A1} (S^{2n+2m+1} \wedge (G_m)^{\wedge 2q}) \Rightarrow Z_{(2)} \otimes π_{i}^{A1, s} (S^{m} \wedge (G_m)^{\wedge q}).$$

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BibTeXRIS

Kirsten Wickelgren, Ben Williams. 2018-11-15. The Simplicial EHP Sequence in A1-Algebraic Topology. https://doi.org/10.2140/gt.2019.23.1691

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